Question

Many elementary school students in a school district currently have ear infections. A random sample of children in two different schools found that 14 of 48 at one school and 12 of 30 at the other had this infection. At the .05 level of significance, is there sufficient evidence to conclude that a difference exists between the proportion of students who have ear infections at one school and the other?

		Yes, there is sufficient information to reject the hypothesis that the proportions of students at the two schools who have ear infections are the same because the test value –9.00 is outside the interval (-1.96,1.96).
		No, there is not sufficient information to reject the hypothesis that the proportions of students at the two schools who have ear infections are the same because the test value –0.99 is inside the interval (-1.96,1.96).
		No, there is not sufficient information to reject the hypothesis that the proportions of students at the two schools who have ear infections are the same because the test value –1.29 is inside the interval (-1.96,1.96).
		Yes, there is sufficient information to reject the hypothesis that the proportions of students at the two schools who have ear infections are the same because the test value –4.99 is outside the interval (-1.96,1.96).

Answer 1

The statistical software output for this problem is:

On the basis of above output:

Test statistic = -0.99

Hence,

No, there is not sufficient information to reject the hypothesis that the proportions of students at the two schools who have ear infections are the same because the test value –0.99 is inside the interval (-1.96,1.96).

Option B is correct.