The manufacturer of an over the counter medication tylenol...

The manufacturer of an over-the-counter medication, Tylenol, claims that its product brings pain relief to headache sufferers in less than 3.5 minutes, on average. In order to be able to make this claim in its television advertisements, the manufacturer was required by a particular television network to present statistical evidence in support of the claim. The manufacturer randomly selected 50 headache sufferers and discovered that the mean time to relief was 3.3 minutes and the standard deviation was 1.1 minutes. Using the 5-step process developed in class, do headache sufferers receive relief in less than 3.5 minutes? Use a significance level of 0.05. What type of error might have been committed? Can the manufacturer run the ad?

Transcript

00:01 All right.

00:02 So we're going to conduct a five -step hypothesis test to test whether headache suffers, received pain relief in less than three -knit minutes.

00:14 So make our assumptions.

00:15 Well, the assumptions are that our data is normally distributed because we have a sample size that's greater than 30.

00:21 And by the central limit theorem, it says if we have a sample size of greater than 30, then the sampling distribution.

00:31 Will be approximately normal.

00:33 So that's our assumption.

00:38 And we're going to use, so now we're going to state our research at null hypotheses.

00:43 They're right here.

00:44 Now i usually start with the alternative, the thing we're testing for, are we significantly less than three and a half minutes? so the alternative hypothesis is that new is less than three and a half.

00:55 Whereas the null is going to be the complement to that, which is greater than equal to 3 .5.

01:02 And you might see this as the mule is me is equal to 3 .5 and that'd be okay too.

01:07 But the key thing is this alternative.

01:10 This is what we're testing for.

01:13 And this also tells us it's a one -tailed test.

01:16 So here's our little distribution.

01:19 Here's where the mean is.

01:20 We're looking, are we significantly to the left of, are we significantly below the mean? the sampling distribution is going to be the student's t distribution.

01:34 And the test statistic is given with the following formula.

01:38 X bar minus the mean of the sampling distribution.

01:40 Over s over root n.

01:44 And we use t because we don't know the population standard deviation.

01:49 If we did, then we could use the z distribution, but we don't, so we're going to use t.

01:54 And we have everything to compute the test statistic.

02:01 We have the mean here.

02:04 The sample means 3 .3.

02:06 We're told that right here.

02:08 And the mean of the sampling distribution is we're going to assume it's 3 .5.

02:14 And the sample standard evasion is 1 .1, sample size is 50.

02:19 Put that in the calculator and we get this t value, negative 1 .2856486.