A researcher wishes to test whether the proportion of college students who smoke

Question

A researcher wishes to test whether the proportion of college students who smoke is the same in four different colleges. She randomly selects 100 students from each college and records the number that smoke. The results are shown below. College A College B College C College D Smoke 17 26 11 34 Don't smoke 83 74 89 66 Use a 0.01 significance level to test the claim that the proportion of students smoking is the same at all four colleges if the test statistic: 2 = 17.832. Select one:

a. Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the proportion of students smoking is the same at all four colleges.

b. Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the proportion of students smoking is the same at all four colleges.

c. Do not reject the null hypothesis. There is in sufficient evidence to warrant rejection of the claim that the proportion of students smoking is the same at all four colleges.

d. Do not reject the null hypothesis. There is insufficient evidence to warrant rejection of the claim that the proportion of students smoking is the same at all four colleges.

Explanation / Answer

at alpha = 0.01, chi-square statistic = 17.8322. The p-value is 0.000476. The result is significant

Pvalue is less than alpha

i.e 0.000476 < 0.01

So, we reject Null hypothesis

Therefore Answer : Option (a)

Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the proportion of students smoking is the same at all four colleges.

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