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## Statistics and probability

### Unit 12: Lesson 4

Tests about a population mean- Writing hypotheses for a significance test about a mean
- Writing hypotheses for a test about a mean
- Conditions for a t test about a mean
- Reference: Conditions for inference on a mean
- Conditions for a t test about a mean
- When to use z or t statistics in significance tests
- Example calculating t statistic for a test about a mean
- Calculating the test statistic in a t test for a mean
- Using TI calculator for P-value from t statistic
- Using a table to estimate P-value from t statistic
- Calculating the P-value in a t test for a mean
- Comparing P-value from t statistic to significance level
- Making conclusions in a t test for a mean
- Free response example: Significance test for a mean

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# Using TI calculator for P-value from t statistic

AP.STATS:

VAR‑7 (EU)

, VAR‑7.E (LO)

, VAR‑7.E.1 (EK)

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.

## Want to join the conversation?

- I do not have that kind of calculator so the only option is using the t table. However, when doing this, I see that the closest value to the given t value of 1,9 is 1.943 and it leads to 0.05. So it seems to be equal to alpha. I want to make sure whether it still means we fail to reject because t table and calculator have different results according to the video?(5 votes)
- When I typed in the exact data like you did into tcdf, I had a problem called SYNTAX. How can I fix it?(1 vote)
- 99% of the time, a syntax error comes from a spelling mistake.

My guess is that you didn't write it*exactly*like Sal did. Maybe you missed a comma or a parenthesis, something like that.(4 votes)

- okay so question: if you need to find P(t not equal to your t statistic) would you use tpdf and what you get from that and you subtract from 1 ??(2 votes)
- How do you get the P value to show up after you enter the data in the tcdf calculator? The P value in the video showed up after Sal did something, I could not see what.(1 vote)
- Sorry to break it to you, but the tcdf function is not meant to give the p-value. tcdf gives the area under the curve (probability) of a t-distribution graph, within the boundaries you selected and df. You can get a p-value by doing an inference test, which can be done by pressing the stat key followed by two clicks to the right. There will be a list of tests, and by putting in your numbers, the calculator will give you a p-value.(2 votes)

- How can I solve the P value if I don't have a TCDF calculator?

I can't find the TCDf on the search engine, so I can't solve practice on Calculating the P - value in a test for a mean.(1 vote) - I use NORMSDIST() to found the p-value having t in Spreadsheets, but it does not give me the same result as Sal. What am i doing wrong?(1 vote)
- I can't find the function on my TI-36. Does it exist, or am I missing it?(1 vote)
- How can i use excel to quantify P-value from t statistic?(0 votes)

## Video transcript

- [Instructor] Miriam was
testing her null hypothesis that the population mean of some data set is equal to 18 versus her
alternative hypothesis is that the mean is less than 18 with a sample of seven observations. Her test statistic, I
can never say that right, was t is equal to negative 1.9. Assume that the conditions
for inference were met. What is the approximate p
value for Miriam's test? So, pause this video and see if you can figure this out on your own. Alright, what I always like
to remind ourselves what's going on here before I go ahead
and calculate the p value. There's some data set,
some population here and the null hypothesis is
that the true mean is 18, the alternative is that it's less than 18. To test that null hypothesis,
Miriam takes a sample, sample size is equal to seven. From that, she would
calculate her sample mean and her sample standard deviation, and from that, she would
calculate this t statistic. The way she would do that or if they didn't tell us ahead
of time what that was. We would say the t statistic
is equal to her sample mean, minus the assumed mean
from the null hypothesis, that's what we have over here, divided by and this is a mouthful, our approximation of the standard error of the mean. The way we get that approximation, we take our sample standard deviation and divide it by the square
root of our sample size. Well, they've calculated
this ahead of time for us. This is equal to negative 1.9. So, if we think about a t distribution, I'll try to hand draw a rough
t distribution really fast, and if this is the mean
of the t distribution, what we are curious about,
because our alternative hypothesis is that the
mean is less than 18. What we care about is,
what is the probability of getting a t value that
is more than 1.9 below the mean so this right
over here, negative 1.9. It's this area, right there. I'm gonna do this with a TI-84, at least an emulator of a TI-84. All we have to do is, we
would go to 2nd distribution and then I would use the t cumulative distribution function so let's go there, that's the number six
right there, click enter. My lower bound... Yeah, I essentially wanted
it to be negative infinity and we can just call
that negative infinity. It's an approximation of negative infinity, very, very low number. Our upper bound would be
negative 1.9, negative 1.9. And then our degrees of freedom, that's our sample size minus one. Our sample size is seven so our degrees of freedom would be six. There we have it. This would be, our p value
would be approximately 0.053. Our p value would be approximately 0.053. Then what Miriam would do is,
would compare this p value to her preset significance
level, to alpha. If this is below alpha,
then she would reject her null hypothesis, which
would suggest the alternative. If this is above alpha, then she would fail to reject her null hypothesis.