Attitudes In the study of older students’ attitudes from Exercise 63, the sample mean SSHA score

step 1 This is problem number 67 from Section 9 .3. And this problem, they're actually telling us to go

Attitudes In the study of older students’ attitudes from...

Key Concepts

One-Sample T-Test

A one-sample t-test is a statistical method used to determine whether the mean of a sample differs significantly from a known or hypothesized population mean. It is particularly useful when the population standard deviation is unknown and the sample size is relatively small, requiring the use of the t-distribution.

Test Statistic

The test statistic in a one-sample t-test measures how far the sample mean is from the hypothesized population mean in units of the standard error. It is calculated by subtracting the hypothesized mean from the sample mean and dividing the result by the standard error, serving as the basis to evaluate the hypothesis.

Standard Error

The standard error is an estimate of the variability of the sample mean and is calculated by dividing the sample standard deviation by the square root of the sample size. It reflects the precision of the sample mean as an estimate of the population mean and is crucial in the computation of the test statistic.

Degrees of Freedom

Degrees of freedom in a one-sample t-test typically equal the sample size minus one. They represent the number of independent pieces of information available for estimating the population variance and are used to determine the appropriate shape of the t-distribution for the hypothesis test.

P-Value

The P-value indicates the probability of obtaining a test statistic at least as extreme as the one calculated from the sample data, assuming that the null hypothesis is true. It is used to assess the strength of the evidence against the null hypothesis, with smaller values suggesting stronger evidence for rejecting it.

Transcript

00:01 This is problem number 67 from section 9 .3.

00:06 And this problem, they're actually telling us to go back to problem 63 to get some information, but they want us to do two things.

00:14 They want us to calculate the test statistic.

00:17 And then from that test statistic, they want us to find the p value using table b, which is your t distribution table.

00:24 And then they want you to go to the calculator and show you know how to find the p value from the calculator.

00:30 So we're going to do all three of those.

00:31 I'm going to have a couple slides on here.

00:34 And so if you need to pause this at any moment, pause the video.

00:37 But i'm going to have the ap formula sheets.

00:41 I need my calculator.

00:44 And then i also need that table b, a t distribution table.

00:48 So if you have those things handy, that'd be nice.

00:50 But first off, to calculate the test statistic.

00:54 Now, we either have a z stat or a t -stat.

00:58 Those are two different test statistics that we have right now, but because we are in a mean, it means that we are going to be looking for a t statistic, a t -statist.

01:11 A t -stat is what we'll call it.

01:13 Now, there is a formula for a t -stat, and we can sort of see it on the formula sheet.

01:20 Here on the formula sheet, it doesn't come right out and tell us, but right down here, standardized test statistic.

01:27 We have this in words.

01:29 Statistics minus parameter divided by standard error of the statistic.

01:35 Now, hopefully we understand what all three of those things are.

01:38 So if i come back over here, again, that was the statistic minus the parameter divided by standard error of stat.

01:52 Now remember, statistic, s, sample.

01:56 The statistic comes from the sample.

01:59 And in our case here, our sample gave us a statistic of 125 .7.

02:07 The parameter, p, population.

02:10 The parameter comes from the population mean, which in problem 63, they told us, was 115.

02:18 And we're going to divide that standard error of the statistic.

02:22 Well, there's a formula for that.

02:24 So i'm going to go back to my formula sheet, and it's going to be on the backside.

02:27 And the new ap formula sheet is actually really nice.

02:31 They have it set up.

02:32 We have our means.

02:34 We're in a one population mean.

02:37 There is standard error.

02:39 So that's my formula.

02:41 Standard deviation divided by square root of n, or the sample standard deviation, divided by square root of n.

02:48 So if i come back over here, we're looking at sample standard deviation.

02:53 They tell me in my problem that the sample standard deviation is 29 .8 divided by the square root of the sample size.

03:07 That's a square root of 45...

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