https://www.khanacademy.org/math/statistics-probability/significance-tests-one-sample/idea-of-significance-tests/v/simple-hypothesis-testing 2020-06-23T07:22:42Z Simple hypothesis testing Sal walks through an example about who should do the dishes that gets at the idea behind hypothesis testing. Sal Khan video https://cdn.kastatic.org/googleusercontent/3kQ6NeK5MkCW_R3YVwsZaQ1j0ge5tgaZFZRbaAYEOAV-4gvmwgBc4tstQlbTaNSm0bZ3-bH757cCSRScfqJaNg Simple hypothesis testing Sal walks through an example about who should do the dishes that gets at the idea behind hypothesis testing. https://cdn.kastatic.org/ka-youtube-converted/5D1gV37bKXY.mp4/5D1gV37bKXY.mp4 385 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/idea-significance-tests/v/idea-behind-hypothesis-testing 2024-01-19T18:37:08.054557436Z Idea behind hypothesis testing The lesson explores hypothesis testing in statistics, demonstrating how varied outcomes from a test with a known accuracy rate can influence the acceptance or rejection of a hypothesis. This understanding is key to evaluating the reliability of statistical tests. video https://cdn.kastatic.org/ka_thumbnails_cache/af78c927-0baf-4729-917f-1ec9f39858ba_1280_720_base.png Idea behind hypothesis testing The lesson explores hypothesis testing in statistics, demonstrating how varied outcomes from a test with a known accuracy rate can influence the acceptance or rejection of a hypothesis. This understanding is key to evaluating the reliability of statistical tests. https://cdn.kastatic.org/ka-youtube-converted/dpGmVV0-4jc.mp4/dpGmVV0-4jc.mp4 469 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/idea-significance-tests/v/examples-of-null-and-alternative-hypotheses 2022-11-16T04:22:43.7414897Z Examples of null and alternative hypotheses The null and alternative hypotheses are both statements about the population that you are studying. The null hypothesis is often stated as the assumption that there is no change, no difference between two groups, or no relationship between two variables. The alternative hypothesis, on the other hand, is the statement that there is a change, difference, or relationship. video https://cdn.kastatic.org/googleusercontent/OXbA1gYSDWaeWJVj0aqC6yyI3SgIRJC2PDyjAx1Llw3ltRyN-jNIM4MH24rpc9TTHpxSXilMIY5m3JFjM8rjDkg Examples of null and alternative hypotheses The null and alternative hypotheses are both statements about the population that you are studying. The null hypothesis is often stated as the assumption that there is no change, no difference between two groups, or no relationship between two variables. The alternative hypothesis, on the other hand, is the statement that there is a change, difference, or relationship. https://cdn.kastatic.org/ka-youtube-converted/_3_6wjycJdk.mp4/_3_6wjycJdk.mp4 342 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/idea-significance-tests/v/p-values-and-significance-tests 2022-11-16T04:22:43.7414897Z P-values and significance tests We compare a P-value to a significance level to make a conclusion in a significance test. Given the null hypothesis is true, a p-value is the probability of getting a result as or more extreme than the sample result by random chance alone. If a p-value is lower than our significance level, we reject the null hypothesis. If not, we fail to reject the null hypothesis. video https://cdn.kastatic.org/googleusercontent/nOw2xiCTIpFBKTmpWTtokdiTCKLtb-RilavA58juAbMNpz8Xak_nd6VA4w33pQAfWeYj25XzvCE87DjXgaWx4tAv P-values and significance tests We compare a P-value to a significance level to make a conclusion in a significance test. Given the null hypothesis is true, a p-value is the probability of getting a result as or more extreme than the sample result by random chance alone. If a p-value is lower than our significance level, we reject the null hypothesis. If not, we fail to reject the null hypothesis. https://cdn.kastatic.org/ka-youtube-converted/KS6KEWaoOOE.mp4/KS6KEWaoOOE.mp4 478 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-quantitative-means/xfb5d8e68:carrying-out-test-mean/v/when-to-use-z-or-t-statistics-in-significance-tests 2022-10-07T00:58:19.561984208Z When to use z or t statistics in significance tests When to use z or t statistics in significance tests video https://cdn.kastatic.org/ka_thumbnails_cache/61292ded-d090-4c95-ae3c-df180adcb318_1280_720_base.png When to use z or t statistics in significance tests When to use z or t statistics in significance tests https://cdn.kastatic.org/ka-youtube-converted/-bhfcBvyWoc.mp4/-bhfcBvyWoc.mp4 291 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/idea-significance-tests/v/comparing-p-value-diff-significance-levels 2022-10-07T00:58:19.561984208Z Comparing P-values to different significance levels Example comparing P-values to different significance levels, and why it's important to set the significance level before a test. video https://cdn.kastatic.org/ka_thumbnails_cache/d2f088de-f17e-40aa-9a91-65105229f636_1280_720_base.png Comparing P-values to different significance levels Example comparing P-values to different significance levels, and why it's important to set the significance level before a test. https://cdn.kastatic.org/ka-youtube-converted/DQCF4kTXf9Q.mp4/DQCF4kTXf9Q.mp4 281 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-quantitative-means/xfb5d8e68:carrying-out-test-mean/v/example-calculating-t-statistic-for-signficance-test 2024-01-19T18:46:06.800206322Z Example calculating t statistic for a test about a mean The lesson demonstrates conducting a t-test for a population mean with a teacher experience sample. It explains the t-statistic calculation and the p-value interpretation to test a null hypothesis. This process helps ascertain if the true mean is less than the hypothesized mean. video https://cdn.kastatic.org/ka_thumbnails_cache/bcedcbed-48bf-4354-9c3d-d9912f61390d_1280_720_base.png Example calculating t statistic for a test about a mean The lesson demonstrates conducting a t-test for a population mean with a teacher experience sample. It explains the t-statistic calculation and the p-value interpretation to test a null hypothesis. This process helps ascertain if the true mean is less than the hypothesized mean. https://cdn.kastatic.org/ka-youtube-converted/BJl9WA787-Q.mp4/BJl9WA787-Q.mp4 302 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/xfb5d8e68:carrying-out-test-proportion/v/calculating-p-value-from-z-table 2022-11-16T04:22:43.7414897Z Calculating a P-value given a z statistic In a significance test about a population proportion, we first calculate a test statistic based on our sample results. We then calculate a p-value based on that test statistic using a normal distribution. video https://cdn.kastatic.org/ka_thumbnails_cache/d1104651-5ea6-4326-9445-0c28e3ea84d4_1280_720_base.png Calculating a P-value given a z statistic In a significance test about a population proportion, we first calculate a test statistic based on our sample results. We then calculate a p-value based on that test statistic using a normal distribution. https://cdn.kastatic.org/ka-youtube-converted/NNpv-n_Hbvc.mp4/NNpv-n_Hbvc.mp4 327 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/one-sample-z-test-proportion/v/conditions-for-a-z-test-about-a-proportion 2022-10-07T00:58:19.561984208Z Conditions for a z test about a proportion Examples showing how to check whether or not the conditions have been met for doing a z test about a proportion. video https://cdn.kastatic.org/ka_thumbnails_cache/98bc0a31-83af-4da6-bcd7-71447262c2d4_1280_720_base.png Conditions for a z test about a proportion Examples showing how to check whether or not the conditions have been met for doing a z test about a proportion. https://cdn.kastatic.org/ka-youtube-converted/5JlJ4Qfk8g4.mp4/5JlJ4Qfk8g4.mp4 333 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/xfb5d8e68:concluding-test-proportion/v/comparing-p-value-to-significance-level-example 2022-10-07T00:58:19.561984208Z Making conclusions in a test about a proportion Example of how to make a conclusion in a test about a proportion video https://cdn.kastatic.org/ka_thumbnails_cache/c3b24e1a-e241-4c34-9486-422ba2a5da2e_1280_720_base.png Making conclusions in a test about a proportion Example of how to make a conclusion in a test about a proportion https://cdn.kastatic.org/ka-youtube-converted/RcjZwZJO5qo.mp4/RcjZwZJO5qo.mp4 314 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/statistics-probability/significance-tests-one-sample/error-probabilities-and-power/v/type-1-errors 2020-06-23T07:22:40Z Type 1 errors A Type 1 error occurs when the null hypothesis is true, but we reject it because of an usual sample result. Sal Khan video https://cdn.kastatic.org/googleusercontent/l4vnk81zegpBNd16Is0jV2BzIJTxP2MwvJZf-XbU7ZR1YNcZ8iq8dNTSpjKanNA2V2hpty-ewdlrn0oN9icQsew Type 1 errors A Type 1 error occurs when the null hypothesis is true, but we reject it because of an usual sample result. https://cdn.kastatic.org/ka-youtube-converted/EowIec7Y8HM.mp4/EowIec7Y8HM.mp4 204 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/error-probabilities-power/v/introduction-to-type-i-and-type-ii-errors 2022-11-16T04:22:43.7414897Z Introduction to Type I and Type II errors Both type 1 and type 2 errors are mistakes made when testing a hypothesis. A type 1 error occurs when you wrongly reject the null hypothesis (i.e. you think you found a significant effect when there really isn't one). A type 2 error occurs when you wrongly fail to reject the null hypothesis (i.e. you miss a significant effect that is really there). video https://cdn.kastatic.org/googleusercontent/Okl0qDRVunIQZp3ZADIl-ExCR38MYhv7apTl6dIf0ykIzYWu0WeBGLysl9lblpx6Jboh_L-tFwA1jiZyAv5iCz4 Introduction to Type I and Type II errors Both type 1 and type 2 errors are mistakes made when testing a hypothesis. A type 1 error occurs when you wrongly reject the null hypothesis (i.e. you think you found a significant effect when there really isn't one). A type 2 error occurs when you wrongly fail to reject the null hypothesis (i.e. you miss a significant effect that is really there). https://cdn.kastatic.org/ka-youtube-converted/Hdbbx7DIweQ.mp4/Hdbbx7DIweQ.mp4 303 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/error-probabilities-power/v/examples-identifying-type-i-and-type-ii-errors 2022-10-07T00:58:19.561984208Z Examples identifying Type I and Type II errors Examples identifying Type I and Type II errors video https://cdn.kastatic.org/googleusercontent/pBQva9CszZX4JZDScd9wUoNw_H8sb6Ent3NnyJ9RyG-8AO1o_yIBnH9n8lUjvqRdz4HTt7zQ_Pp-H1yQ_sxQUEY Examples identifying Type I and Type II errors Examples identifying Type I and Type II errors https://cdn.kastatic.org/ka-youtube-converted/JNOWWJeZBTc.mp4/JNOWWJeZBTc.mp4 344 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/one-sample-z-test-proportion/v/constructing-hypotheses-for-a-significance-test 2022-10-07T00:58:19.561984208Z Constructing hypotheses for a significance test about a proportion Constructing hypotheses for a significance test about a proportion video https://cdn.kastatic.org/ka_thumbnails_cache/39853782-262b-412b-8291-ce5b0c583aff_1280_720_base.png Constructing hypotheses for a significance test about a proportion Constructing hypotheses for a significance test about a proportion https://cdn.kastatic.org/ka-youtube-converted/8MJvK26PwSo.mp4/8MJvK26PwSo.mp4 256 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-quantitative-means/one-sample-t-test-mean/v/writing-hypotheses-for-significance-test-about-means 2022-10-07T00:58:19.561984208Z Writing hypotheses for a significance test about a mean Example of constructing hypotheses for a test about a mean video https://cdn.kastatic.org/ka_thumbnails_cache/72a9061c-1525-4da6-92bb-5e70626cca63_1280_720_base.png Writing hypotheses for a significance test about a mean Example of constructing hypotheses for a test about a mean https://cdn.kastatic.org/ka-youtube-converted/89Dp9Xq4eaA.mp4/89Dp9Xq4eaA.mp4 154 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-quantitative-means/one-sample-t-test-mean/e/writing-hypotheses-one-sample-t-test-mean 2021-07-01T02:19:29Z Writing hypotheses for a test about a mean Practice writing the null and alternative hypotheses in a one-sample t test for a mean Jeff Dodds exercise https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/one-sample-z-test-proportion/e/writing-hypotheses-one-sample-z-test-proportion 2021-07-01T02:19:29Z Writing hypotheses for a test about a proportion Practice writing the null and alternative hypotheses in a one sample z test for a proportion Jeff Dodds exercise https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/idea-significance-tests/e/writing-null-and-alternative-hypotheses-informal 2021-07-01T02:19:28Z Writing null and alternative hypotheses Practice writing null and alternative hypotheses for a significance test Jeff Dodds exercise https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/one-sample-z-interval-proportion/a/conditions-inference-one-proportion 2021-07-01T02:19:27Z Reference: Conditions for inference on a proportion article https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/idea-significance-tests/a/p-value-conclusions 2021-07-01T02:19:30Z Using P-values to make conclusions Learn how to use a P-value and the significance level to make a conclusion in a significance test. article https://www.khanacademy.org/math/statistics-probability/significance-tests-one-sample/idea-of-significance-tests/e/hypothesis-testing-with-simulations 2026-04-08T01:15:04.085520103Z Simple hypothesis testing Show that you have mastery over the idea behind hypothesis testing by calculating some probabilities and drawing conclusions. Tomer Gal exercise https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/xfb5d8e68:concluding-test-proportion/e/conclusions-one-sample-z-test-proportion 2021-07-01T02:19:29Z Making conclusions in a z test for a proportion Make conclusions in a one-sample z test for a proportion based on the P-value and significance level. Jeff Dodds exercise https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/error-probabilities-power/e/type-i-error-type-ii-error-power 2023-01-17T23:38:14.782841713Z Type I vs Type II error Distinguish between Type I and Type II error in context. Jeff Dodds exercise https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-data/cc-8th-scatter-plots/v/constructing-scatter-plot 2023-05-12T21:01:01.897246564Z Constructing a scatter plot Does the time an exam happens affects the scores? Aubrey gathered info. Then she made a scatter plot with the time of day on the bottom (on the horizontal axis) and the scores on the side (on the vertical axis). She didn't find a clear pattern. Sal Khan video https://cdn.kastatic.org/googleusercontent/Kboi5qiegn6DQdifmcZsrrlizFXNWb2EFH_OX1hqmURDk4A-BRDbSTJYb443ZQ4I6YR610NhKilfi6z6PkcaRw Constructing a scatter plot Does the time an exam happens affects the scores? Aubrey gathered info. Then she made a scatter plot with the time of day on the bottom (on the horizontal axis) and the scores on the side (on the vertical axis). She didn't find a clear pattern. https://cdn.kastatic.org/ka-youtube-converted/sHbX58y5D4U.mp4/sHbX58y5D4U.mp4 152 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-data/cc-8th-interpreting-scatter-plots/v/scatter-plot-interpreting 2023-05-12T21:01:01.897246564Z Example of direction in scatterplots There are two graphs. One shows the relationship between study time and test grades. Do you get better grades if you study more? The other graph shows the relationship between shoe size and grades. Do you get better grades if you wear larger shoes? Sal Khan video https://cdn.kastatic.org/googleusercontent/J3SG8_hb2g42LxU8pjd5yJdCsO84WNLVJqSqhvz9w4o5rcA-t-4NcYXoSEtLESjpZGx_JOtdja2p4sBuaREk15Sw Example of direction in scatterplots There are two graphs. One shows the relationship between study time and test grades. Do you get better grades if you study more? The other graph shows the relationship between shoe size and grades. Do you get better grades if you wear larger shoes? https://cdn.kastatic.org/ka-youtube-converted/Jpbm5YgciqI.mp4/Jpbm5YgciqI.mp4 146 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/statistics-probability/describing-relationships-quantitative-data/introduction-to-scatterplots/a/constructing-and-interpreting-a-scatterplot 2021-04-29T07:52:14Z Positive and negative associations in scatterplots article https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-data/cc-8th-scatter-plots/e/constructing-scatter-plots 2026-06-30T21:20:50.424509082Z Constructing scatter plots Practice plotting points to construct a scatter plot. Tomer Gal exercise https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-data/cc-8th-scatter-plots/e/making-good-scatter-plots 2021-07-01T02:19:31Z Making appropriate scatter plots An appropriate scatter plot has the independent variable on the x-axis and the dependent variable on the y-axis. Also, the scale of both axes should be reasonable, making the data as easy to read as possible. In these practice problems, we practice telling good scatter plots from bad ones. Jeff exercise https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-data/cc-8th-interpreting-scatter-plots/e/positive-and-negative-linear-correlations-from-scatter-plots 2026-07-01T17:20:51.245763889Z Positive and negative linear associations from scatter plots Practice identifying the types of associations shown in scatter plots. Sometimes we see linear associations (positive or negative), sometimes we see non-linear associations (the data seems to follow a curve), and other times we don't see any association at all. Jeff exercise https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-data/cc-8th-interpreting-scatter-plots/e/interpreting-scatter-plots 2026-06-30T23:50:44.491483867Z Describing trends in scatterplots Practice making sense of trends in scatterplots. That is, explain what trends mean in terms of real-world quantities. Tomer Gal exercise https://www.khanacademy.org/math/ap-statistics/bivariate-data-ap/scatterplots-correlation/v/bivariate-relationship-linearity-strength-and-direction 2022-10-07T00:58:19.561984208Z Bivariate relationship linearity, strength and direction Describe a bivariate relationship's linearity, strength, and direction video https://cdn.kastatic.org/ka_thumbnails_cache/9a462c1b-305b-4d4a-9e3a-78326881823a_1280_720_base.png Bivariate relationship linearity, strength and direction Describe a bivariate relationship's linearity, strength, and direction https://cdn.kastatic.org/ka-youtube-converted/30LcZqRfPRY.mp4/30LcZqRfPRY.mp4 493 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-data/cc-8th-line-of-best-fit/v/estimating-the-line-of-best-fit-exercise 2023-05-12T21:01:01.897246564Z Estimating the line of best fit exercise The "line of best fit" is a line that shows the pattern of data points. If we can find a good line, it means there is a linear trend. If not, it means there is no linear trend. We can't ignore points that don't fit the trend. Sal Khan video https://cdn.kastatic.org/googleusercontent/yMNzEamJCQT7A1xvGsloyZpWmvtEQ2nBGFUkm3ccmtXOwVO0Q6DuShSdnqkmswqKPzYy2i8z1R8VYXresfBm2SU Estimating the line of best fit exercise The "line of best fit" is a line that shows the pattern of data points. If we can find a good line, it means there is a linear trend. If not, it means there is no linear trend. We can't ignore points that don't fit the trend. https://cdn.kastatic.org/ka-youtube-converted/ioieTr41L24.mp4/ioieTr41L24.mp4 77 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-data/cc-8th-line-of-best-fit/v/smoking-1945-extrapolation 2023-05-12T21:01:01.897246564Z Line of best fit: smoking in 1945 The scatter plot shows how many adults in America smoked from year to year. We can guess how many smoked in 1945 by drawing a line that slopes down through the points. Then we see how high the line would be 20 years earlier. Sal Khan video https://cdn.kastatic.org/googleusercontent/yZKpVENPaJ0cbI753S0lV0n5d0Bn6Hvs8N4MtCyo9VXE_X59LGtcs5xHl0jUv294K8q-S8pg6YeAVll59ZXn9-6d Line of best fit: smoking in 1945 The scatter plot shows how many adults in America smoked from year to year. We can guess how many smoked in 1945 by drawing a line that slopes down through the points. Then we see how high the line would be 20 years earlier. https://cdn.kastatic.org/ka-youtube-converted/d4WE4SnhBDU.mp4/d4WE4SnhBDU.mp4 287 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-data/cc-8th-line-of-best-fit/e/plotting_the_line_of_best_fit 2026-03-31T14:59:02.026924717Z Eyeballing the line of best fit Given a random assortment of points, draw a line of best fit through them. Sid Patel exercise https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-data/cc-8th-line-of-best-fit/e/linear-models-of-bivariate-data 2026-05-04T16:10:46.51963925Z Estimating slope of line of best fit Given a scatter plot, can you estimate the slope of the line of best fit that goes through the data points? pstinchcombe exercise https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-data/cc-8th-line-of-best-fit/e/equations-of-lines-of-best-fit-to-make-predictions 2023-12-11T22:13:00.981327266Z Estimating equations of lines of best fit, and using them to make predictions Practice estimating the equation of a line of best fit through data points in a scatter plot. Then, use the equation to make a prediction. Jeff exercise https://www.khanacademy.org/math/statistics-probability/significance-tests-one-sample/more-significance-testing-videos/v/z-statistics-vs-t-statistics 2020-06-23T07:22:40Z Z-statistics vs. T-statistics Sal breaks down the difference between Z-statistics and T-statistics. Sal Khan video https://cdn.kastatic.org/googleusercontent/ISEkpRmpFazzyAdOeSV3qXl_FI0bhehF3MXjftZ9z7S5BxICt4rVFXcN54C69QqzHUqRAvgBLKCpTS0CXNEhXyc Z-statistics vs. T-statistics Sal breaks down the difference between Z-statistics and T-statistics. https://cdn.kastatic.org/ka-youtube-converted/5ABpqVSx33I.mp4/5ABpqVSx33I.mp4 399 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/statistics-probability/significance-tests-confidence-intervals-two-samples/comparing-two-proportions/v/comparing-population-proportions-1 2020-06-23T07:22:40Z Comparing population proportions 1 Sal uses an election example to compare population proportions. Sal Khan video https://cdn.kastatic.org/googleusercontent/DXzEcT_r9RoJRA4GUzJBtl6JT1RP6rXz0sdfN-gYgCKiK7HWzGuLU945vuWCsRksRaavGC358gFSpxRHIVBc6VfS Comparing population proportions 1 Sal uses an election example to compare population proportions. https://cdn.kastatic.org/ka-youtube-converted/a1Ye5RcWOqg.mp4/a1Ye5RcWOqg.mp4 647 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/statistics-probability/significance-tests-confidence-intervals-two-samples/comparing-two-proportions/v/comparing-population-proportions-2 2020-06-23T07:22:40Z Comparing population proportions 2 Sal continues the election example for population proportions. Sal Khan video https://cdn.kastatic.org/googleusercontent/_WSd5qBFFuMeWR1K2DJKKtFSBZHq0WMCVXUOfzanB8-va1i8iKXJqku6TIlVnWzCg0rTp28N1GCvh3nPXbC2ZMHr Comparing population proportions 2 Sal continues the election example for population proportions. https://cdn.kastatic.org/ka-youtube-converted/MNbat1lrJW4.mp4/MNbat1lrJW4.mp4 600 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/statistics-probability/significance-tests-confidence-intervals-two-samples/comparing-two-proportions/v/hypothesis-test-comparing-population-proportions 2021-02-26T18:37:37Z Hypothesis test comparing population proportions Once again, Sal continues the discussion of election results to run a hypothesis test comparing population proportions. Sal Khan video https://cdn.kastatic.org/googleusercontent/V4Ei974H1CAOJgggbcrMM6S3FktCEx3O7GD2zFVbEPkiYVY9f62y8ek9_w-jPO5qtsNdM21_orc57VkYiAhY9Blj Hypothesis test comparing population proportions Once again, Sal continues the discussion of election results to run a hypothesis test comparing population proportions. https://cdn.kastatic.org/ka-youtube-converted/dvSa_tx04hw.mp4/dvSa_tx04hw.mp4 973 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-quantitative-means/xfb5d8e68:carrying-out-test-mean/v/using-ti-calculator-for-p-value-from-t-statistic 2022-11-16T04:22:43.7414897Z Using TI calculator for P-value from t statistic In a significance test about a population mean, we first calculate a test statistic based on our sample results. We can then use technology to calculate the p-value based on that test statistic using a t distribution with n-1 degrees of freedom. video https://cdn.kastatic.org/ka_thumbnails_cache/f1dae93a-63fe-46a5-a27e-ef38b4364873_1280_720_base.png Using TI calculator for P-value from t statistic In a significance test about a population mean, we first calculate a test statistic based on our sample results. We can then use technology to calculate the p-value based on that test statistic using a t distribution with n-1 degrees of freedom. https://cdn.kastatic.org/ka-youtube-converted/M2P96TJMEaM.mp4/M2P96TJMEaM.mp4 199 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-quantitative-means/xfb5d8e68:carrying-out-test-mean/v/calculating-p-value-from-t-statistic 2022-11-16T04:22:43.7414897Z Using a table to estimate P-value from t statistic In a significance test about a population mean, we first calculate a test statistic based on our sample results. We can then use a table to estimate the p-value based on that test statistic using a t distribution with n-1 degrees of freedom. video https://cdn.kastatic.org/ka_thumbnails_cache/bb0a485b-7a0a-49da-bf4b-e24c9b5e73a7_1280_720_base.png Using a table to estimate P-value from t statistic In a significance test about a population mean, we first calculate a test statistic based on our sample results. We can then use a table to estimate the p-value based on that test statistic using a t distribution with n-1 degrees of freedom. https://cdn.kastatic.org/ka-youtube-converted/z-HSsVARNnk.mp4/z-HSsVARNnk.mp4 293 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-quantitative-means/two-sample-t-test-means/v/example-of-hypotheses-for-paired-and-2-sample-t-tests 2022-10-07T02:10:10.749739204Z Example of hypotheses for paired and two-sample t tests Example of hypotheses for paired and two-sample t tests video https://cdn.kastatic.org/googleusercontent/fy-R_76ajzSrytevQfoLd03ySM4iFRijBsWNteNufDJPntAP8qfMjqwthT-dBmt3pWXu4aL8rocvqUPj7c_iqbiB Example of hypotheses for paired and two-sample t tests Example of hypotheses for paired and two-sample t tests https://cdn.kastatic.org/ka-youtube-converted/X0gIJUXz6jc.mp4/X0gIJUXz6jc.mp4 229 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-quantitative-means/two-sample-t-test-means/v/alternative-hypothesis-for-2-sample-t-test 2022-10-07T02:10:10.749739204Z Hypotheses for a two-sample t test Example of how to write hypotheses for a two-sample t test, and how to distinguish between paired and two-sample comparisons between means. video https://cdn.kastatic.org/googleusercontent/tLeKgY003UR7SmK3CAghd_Ey4Yv2ahwIl5g1bQ9N3Gn05zwiskOtAOxi5ATsdZD8GMrbNuO7lT6MaK6NbavGBSyq Hypotheses for a two-sample t test Example of how to write hypotheses for a two-sample t test, and how to distinguish between paired and two-sample comparisons between means. https://cdn.kastatic.org/ka-youtube-converted/8CJ-RsoYbg0.mp4/8CJ-RsoYbg0.mp4 240 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/probability/xa88397b6:scatterplots/estimating-trend-lines/v/correlation-and-causality 2021-07-15T19:03:52Z Correlation and causality Understanding why correlation does not imply causality (even though many in the press and some researchers often imply otherwise) Sal Khan video https://cdn.kastatic.org/googleusercontent/5CfPXW2BNtAmRRtP9dG_YYdpR_lzzyb0FAtyPGpMonebKXfUYVJfUm7hqHf5RC027L-XXXtNedSPhQDJkXR3TT-b Correlation and causality Understanding why correlation does not imply causality (even though many in the press and some researchers often imply otherwise) https://cdn.kastatic.org/ka-youtube-converted/ROpbdO-gRUo.mp4/ROpbdO-gRUo.mp4 645 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/ap-statistics/bivariate-data-ap/correlation-coefficient-r/v/correlation-coefficient-intuition-examples 2022-10-07T00:58:19.561984208Z Example: Correlation coefficient intuition Sal explains the intuition behind correlation coefficients and does a problem where he matches correlation coefficients to scatter plots. video https://cdn.kastatic.org/ka_thumbnails_cache/eaac8aca-ccd5-4fce-b5bf-f3959d063246_1280_720_base.png Example: Correlation coefficient intuition Sal explains the intuition behind correlation coefficients and does a problem where he matches correlation coefficients to scatter plots. https://cdn.kastatic.org/ka-youtube-converted/-Y-M9aD_ccQ.mp4/-Y-M9aD_ccQ.mp4 441 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/ap-statistics/bivariate-data-ap/correlation-coefficient-r/v/calculating-correlation-coefficient-r 2022-11-16T04:22:43.7414897Z Calculating correlation coefficient r The most common way to calculate the correlation coefficient (r) is by using technology, but using the formula can help us understand how r measures the direction and strength of the linear association between two quantitative variables. video https://cdn.kastatic.org/ka_thumbnails_cache/6226d103-bbc1-48be-b931-6165f68dd982_1280_720_base.png Calculating correlation coefficient r The most common way to calculate the correlation coefficient (r) is by using technology, but using the formula can help us understand how r measures the direction and strength of the linear association between two quantitative variables. https://cdn.kastatic.org/ka-youtube-converted/u4ugaNo6v1Q.mp4/u4ugaNo6v1Q.mp4 742 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/statistics-probability/inference-categorical-data-chi-square-tests/chi-square-goodness-of-fit-tests/v/pearson-s-chi-square-test-goodness-of-fit 2020-06-23T07:22:42Z Pearson's chi square test (goodness of fit) Sal uses the chi square test to the hypothesis that the owner's distribution is correct. Sal Khan video https://cdn.kastatic.org/googleusercontent/tyt9FnA3O2qKZdXZlIfXFWT7VTxtafl9ksU3-QFMAm8DKaAmGh24IO2nn17_GRY6zq_2Lu9xJhi3eOVkWE_N47Y Pearson's chi square test (goodness of fit) Sal uses the chi square test to the hypothesis that the owner's distribution is correct. https://cdn.kastatic.org/ka-youtube-converted/2QeDRsxSF9M.mp4/2QeDRsxSF9M.mp4 708 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/statistics-probability/describing-relationships-quantitative-data/scatterplots-and-correlation/a/correlation-coefficient-review 2024-11-11T03:02:04.50965229Z Correlation coefficient review The correlation coefficient r measures the direction and strength of a linear relationship. Calculating r is pretty complex, so we usually rely on technology for the computations. We focus on understanding what r says about a scatterplot. article https://www.khanacademy.org/math/ap-statistics/bivariate-data-ap/correlation-coefficient-r/e/correlation-coefficient-intuition 2026-04-08T01:15:04.085520103Z Correlation coefficient intuition Match correlation coefficients to scatterplots to build a deeper intuition behind correlation coefficients. . exercise https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/xfb5d8e68:carrying-out-test-proportion/v/calculating-a-z-statistic-in-a-significance-test 2022-10-07T00:58:19.561984208Z Calculating a z statistic in a test about a proportion Calculating a z statistic in a one-sample z test about a proportion video https://cdn.kastatic.org/ka_thumbnails_cache/3dffb5f4-3a25-4626-a915-3ad81f09647c_1280_720_base.png Calculating a z statistic in a test about a proportion Calculating a z statistic in a one-sample z test about a proportion https://cdn.kastatic.org/ka-youtube-converted/DfpFfIdwcIo.mp4/DfpFfIdwcIo.mp4 291 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-quantitative-means/xfb5d8e68:carrying-out-test-mean/v/comparing-p-value-from-t-statistic-to-significance-level 2022-10-07T00:58:19.561984208Z Comparing P-value from t statistic to significance level Example showing how to compare the P-value to a significance level to make a conclusion in a t test. video https://cdn.kastatic.org/ka_thumbnails_cache/e8692e6b-176c-40d4-bc6e-65404d7b2eef_1280_720_base.png Comparing P-value from t statistic to significance level Example showing how to compare the P-value to a significance level to make a conclusion in a t test. https://cdn.kastatic.org/ka-youtube-converted/I5WSC_iRtwE.mp4/I5WSC_iRtwE.mp4 219 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-quantitative-means/one-sample-t-test-mean/v/conditions-t-test-mean 2022-10-07T00:58:19.561984208Z Conditions for a t test about a mean Example showing how to check which conditions have been met for a t test about a mean video https://cdn.kastatic.org/ka_thumbnails_cache/48d4e55e-af37-4fa2-9266-d6b4d7aabaf1_1280_720_base.png Conditions for a t test about a mean Example showing how to check which conditions have been met for a t test about a mean https://cdn.kastatic.org/ka-youtube-converted/GtokpL4f32s.mp4/GtokpL4f32s.mp4 348 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:prepare-for-the-2022-ap-statistics-exam/prepare-for-ap-stats-exam/v/ap-statistics-free-response-on-significance-test-for-mean 2021-07-01T02:19:38Z Free response example: Significance test for a mean AP Statistics free response on significance test for a mean video https://cdn.kastatic.org/googleusercontent/-tvrRoZPm3dEZGh69c5f2xvufhCe8rMzwZWFNIdWBAJhxfPV_9Z-l6cFSuon8H1Mc58CRZ3FWz-TFDiFRmSCg76r Free response example: Significance test for a mean AP Statistics free response on significance test for a mean https://cdn.kastatic.org/ka-youtube-converted/8nCsnsD8Fnw.mp4/8nCsnsD8Fnw.mp4 713 Basic statistical hypothesis testing, test of differences, test of relationships and simple linear regression https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/xfb5d8e68:carrying-out-test-proportion/e/p-value-one-sample-z-test-p 2023-02-22T03:54:13.328982673Z Calculating the P-value in a z test for a proportion Given sample results and the test statistic, practice calculating the P-value in a one-sample z test for a proportion. Jeff Dodds exercise https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/one-sample-z-test-proportion/e/checking-conditions-one-sample-z-test-proportion 2023-06-09T19:33:20.614181298Z Conditions for a z test about a proportion Check whether or not the the conditions have been met for a one sample z test for a proportion Jeff Dodds exercise https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-quantitative-means/xfb5d8e68:carrying-out-test-mean/e/p-value-t-test-mean 2021-07-01T02:19:30Z Calculating the P-value in a t test for a mean Practice calculating the P-value in a one-sample t test for a mean Jeff Dodds exercise https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/xfb5d8e68:carrying-out-test-proportion/e/test-stat-one-sample-z-test-p 2021-07-01T02:19:29Z Calculating the test statistic in a z test for a proportion Practice using sample data to calculate the test statistic in a one-sample z test for a proportion. Jeff Dodds exercise https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-quantitative-means/xfb5d8e68:carrying-out-test-mean/e/test-statistic-t-test 2021-07-01T02:19:34Z Calculating the test statistic in a t test for a mean Practice calculating the test statistic in a one-sample t test for a mean Jeff Dodds exercise