Phoebe has a theory that older students at her high school are more likely to bring a bag lunch than younger students, because they have grown tired of cafeteria food. she takes a simple random sample of 80 sophomores and finds that 52 of them bring a bag lunch. a simple random sample of 104 seniors reveals that 78 of them bring a bag lunch. letting p1= proportion of sophomores who bring a bag lunch, and p2= proportion of seniors who bring a bag lunch, phoebe tests the hypotheses

It appears that the older students bring there lunch more than the younger students.

For the sophomores, the amount is 52 out of 80 or 65%.
For the seniors, the amount is 78 out of 104 or 75%.

From this simple measure, the seniors are bringing their lunch more.

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topeadeniran2 topeadeniran2 · Answer 2 · 2022-03-15T15:27:06+01:00

It should be noted that the p-value will be 0.0713.

How to calculate the p value

From the information given, the following can be deduced:

n1 = 80

n2 = 104.

x1 = 52

x2 = 78

p1 = 52/80 = 0.65

p2 = 78/104 = 0.75

In this case, the test statistics will be Z = -1 466 from the standard normal table. Therefore, the p-value will be P(Z < -1.466) = 0.0713.

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