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 Hypothesis testing 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 Hypothesis testing 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 Hypothesis testing 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 Hypothesis testing 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 Hypothesis testing 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 Hypothesis testing 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 Hypothesis testing 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 Hypothesis testing 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 Hypothesis testing 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 Hypothesis testing 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 Hypothesis testing 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 Hypothesis testing 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 Hypothesis testing 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 Hypothesis testing 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 Hypothesis testing 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/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/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/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/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/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/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