Question

In: Statistics and Probability

An insurance company would like to test the hypothesis that a difference exists in the proportion...

An insurance company would like to test the hypothesis that a difference exists in the proportion of students in 12th grade who text while driving when compared to the proportion of

11th-grade drivers who text. A random sample of 160 12th grade students found that 84 texted while driving. A random sample of 175 11th grade students found that 84 texted while driving. A random sample of 175 12th grade drivers and Population 2 is defined as 11th-grade drivers. What is the 95% confidence interval for the difference in population proportions?

A.

​(−​0.119,​0.369)

B.

​(0.019, 0.231)

C.

​(−​0.037,​0.287)

D.

​(0.103, 0.147)

Solutions

Expert Solution

let p1 be the proportion denoting the proportion of 12th grade students and p2 be the proportion denoting 11th grade students.

According to data given in the question

p1 = 84/160 = 0.525 and n1 = 160 (sample size)

p2 = 70/175 = 0.40, n2 = 175 (sample size)

we have to find 95% confidence interval for proportion difference

z critical value for 95% confidence interval is 1.96 (using z distribution table)

Formula for the confidence interval is given as

setting the given values, we get

this gives us

Therefore, option B is correct answer for the required 95% confidence interval

orchestra answered 2 years ago
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