Test the given claim. If we use the body temperatures from 8...

Test the given claim. If we use the body temperatures from 8 AM on Day 2 as listed in Data Set 3 "Body Temperatures" in Appendix $B$, we get the statistics given in the accompanying table. Use these data with a 0.05 significance level to test the claim that men have body temperatures that vary more than the body temperatures of women.

Test the given claim.
If we use the body temperatures from 8 AM on Day 2 as listed in Data Set 3 "Body Temperatures" in Appendix $B$, we get the statistics given in the accompanying table. Use these data with a 0.05 significance level to test the claim that men have body temperatures that vary more than the body temperatures of women.

Key Concepts

Hypothesis Testing

Hypothesis testing is the procedure used to decide whether the data at hand sufficiently support a particular claim or hypothesis about a population parameter. It involves formulating a null hypothesis that represents a default position, and an alternative hypothesis that represents the claim to be tested.

Null and Alternative Hypotheses

The null hypothesis (H0) and the alternative hypothesis (H1) are the two competing statements in a hypothesis test. In comparing two population variances, the null hypothesis might state that the variances are equal, while the alternative hypothesis could claim that one variance is greater than the other, reflecting the specific claim being tested.

F-test for Variance

The F-test is a statistical test used to compare two variances by taking the ratio of the two sample variances. It helps determine whether the observed difference in variability between two populations is statistically significant, under the assumption that the samples come from normally distributed populations.

Significance Level

The significance level, often denoted by alpha (?), is the threshold used to decide whether to reject the null hypothesis. In this context, a 0.05 significance level indicates a 5% risk of committing a Type I error, meaning there is a 5% chance of rejecting the null hypothesis when it is actually true.

Assumptions for Variance Comparison

For tests like the F-test to be valid, certain assumptions must be met, such as the data being sampled from normally distributed populations and the observations being independent. Ensuring these assumptions helps guarantee the reliability of the test's conclusions.

Transcript

00:01 All righty, guys.

00:03 The first thing we need to do for this problem here is this.

00:06 We need to identify the null alternative hypothesis.

00:08 The null hypothesis is that the variance is the same.

00:11 But if we read the question carefully, alternative hypothesis should be that the variance in male body temperature is greater than the variance in female body temperature.

00:20 So we need to be careful about that.

00:23 Okay, so we'll start there.

00:24 The next thing we're going to do is this.

00:27 We are going to go ahead and look at everything.

00:30 Look at everything given to us.

00:32 So our first standard deviation given to us is 0 .89.

00:37 Our second standard deviation in the problem is 0 .66, which makes s1 squared 0 .89 squared because, excuse me, s1 squared is the standard deviation that's bigger.

00:50 So what we're going to do is we're going to take that and multiply by itself.

00:54 That's s1 squared.

00:55 S2 squared is we're going to take the smaller one and multiply by itself.

00:59 Notice how i'm using the asterisk.

01:00 And google sheets for calculation.

01:03 And yes, i'm using google sheets.

01:04 It will help me in the long run in solving this problem.

01:10 Okay, so those are our two variances right there.

01:14 Okay...