Question

The top food snacks consumed by adults aged 18-54 are gum, chocolate candy, fresh fruit, potato chips, breath mints/candy, ice cream, nuts, cookies, bars, yogurt, and crackers. Out of a random sample of 24 men, 11 ranked fresh fruit in their top five snack choices. Out of a random sample of 37 women, 27 ranked fresh fruit in their top five snack choices. Is there a difference in the proportion of men and women who rank fresh fruit in their top five list of snacks?

Calculate the test statistic.

I already know the p-value = 0.030

Answer 1

Here

sample proportion of men who ranked fresh fruit in their top five snack choices

and sample size of men n₁ = 24

sample proportion of women who ranked fresh fruit in their top five snack choices

and sample size of women n₂ = 37

To test if there is a difference in the proportion of men and women who rank fresh fruit in their top five list of snacks

i.e. to test against

The test statistic can be written as

which under H₀ follows a standard normal distribution.

Now,

The value of the test statistic (ans)