A survey by a magazine stated that 14% of men said they used...

A survey by a magazine stated that 14% of men said they used exercise to reduce stress. A random sample of 100 men was selected and 10 said that they used exercise to relieve stress. Use the graphing calculator to find the test statistic. (Round answer to two decimal places.) A survey by a magazine stated that 14% of men said they used exercise to reduce stress. A random sample of 100 men was selected and 10 said that they used exercise to relieve stress. Test the claim using ? = 0.10. There is enough evidence to reject the null hypothesis. The claim is true. There is enough evidence to reject the null hypothesis. The claim is false. There is not enough evidence to reject the null hypothesis. The claim is probably true. There is not enough evidence to reject the null hypothesis. The claim is probably false.

Transcript

00:01 We want to test a claim made by a magazine that 14 % of men use exercise to reduce stress.

00:07 So let's start with our null and alternative hypotheses.

00:14 The claim that has been made is that p, population proportion, is 14%.

00:19 The null hypothesis always has an equal sign.

00:23 So we'll put that here.

00:25 The alternative hypothesis will be that it's something different.

00:29 So we'll put p is not 14%.

00:31 We have no indication of directionality here.

00:35 We don't have anything saying it will be less than that or it will be more than that.

00:39 So we'll just do not equal to.

00:43 For our sample, we have a sample size of 100.

00:47 And out of that, 10 meet the criteria, which is a sample proportion, 10 out of 100, of 0 .1.

00:54 What is the test statistic? so this is based on assuming that the null hypothesis is true.

01:01 The central limit theorem covers normal approximations for sampling distributions.

01:07 If i took every sample of this size, took all of the sample proportions and plotted them out, i would have something approximately normal.

01:16 It follows a normal distribution.

01:17 Its mean is p.

01:19 Its standard deviation, root p, 1 minus p over n.

01:23 If you're wondering where those come from, look at the mean and standard deviation of the binomial, np and root np or minus p, respectively.

01:31 Divide those by n, you get these.

01:33 The same way we divided number of success states by n to get proportion.

01:40 So we're going to have two rejection regions here.

01:43 This is a two -tailed test.

01:45 We care if our statistic is significantly low or significantly high.

01:52 The test statistic is the standard score for our particular sample proportion.

01:58 It's z score.

01:59 Z tells you how many standard deviations away from a mean a value is in its distribution.

02:06 So here, the raw value is p hat.

02:08 The mean of this distribution is p, which we're pretending is 0 .14.

02:13 Its standard deviation, root p, 1 minus p over n...

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