According to a july 1214 2017 survey of american adults ages...

According to a July 12-14, 2017, survey of American adults ages 18 or older, October is the most popular month to get the flu vaccine. Harris Poll conducted the survey on behalf of CVS Pharmacy with the following results for when Americans get vaccinated: September, 21%; October, 30%; November, 17%; other months, 32%. A random sample of 80 students at your college that received a flu vaccine were distributed according to the month they were vaccinated as follows: September, 6; October, 10; November, 15; other months, 49. At the 0.05 level of significance, is there sufficient reason to indicate that the month that students at your college receive their flu vaccine is distributed differently than the CVS survey?

Transcript

00:01 For this problem, we want to do a chi -squared test for independence, where our null hypothesis is that the month and the number of flu vaccines distributed are independent, and the alternative hypothesis that the two factors are dependent.

00:27 So our test statistic, the titular chi -squared statistic, is equal to the sum over all of the categories, so sum from i equals 1 up to k, of the observed frequency for that category, oi, minus the expected frequency, ei, squared, divided by the expected frequency.

00:48 Now we have that our expected frequencies, or our theorized proportions, oh actually i do need to correct myself here, we're doing a chi -squared test, but actually we're not doing a test for independence, we're doing a goodness of fit test.

01:05 So, pardon me.

01:06 Under our null hypothesis, we have that the proportions are equal to 0 .21, 0 .3, 0 .17, and 0 .32, and then the alternative hypothesis would be that the proportions are not the hypothesized proportions.

01:32 So what i'll do next is jump over into excel, just to make the calculation a little bit quicker here.

01:38 Alright, so i'll copy down the expected, or actually, what i'll do here is i'll calculate out the expected frequencies as i'm going along here.

01:48 We have 0 .21 times 80 for september, we'd expect 0 .3 times 80 for october, expect 0 .17 times 80 for november, and we'd expect 0 .32 times 80 for other.

02:02 Now that we have the expected frequencies, we have the observed frequencies, we just copy down from the table.

02:08 Oops, going the wrong direction there.

02:11 So we have 6, 10, 15, and 49...

Question

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