Question

A store serves two ice cream flavors: vanilla and chocolate. Out of a sample of 50 customers, 27 purchased the vanilla flavor. Assume the underlying customer flavor selection distribution is normal.

Is the proportion of customers purchasing vanilla greater than 50%? (this part is done)

Ho is that p is not greater than 1/2

Ha is that p is greater than 1/2

z = 0.60

p value = 0.30

alpha = significance level = 10%

What is the power of the test if the true population proportion is equal to the sample proportion? (I need help on this part of the question)

Answer 1

Hypotheses are:

Test is right tailed so critical value of z is 1.28.

The critical value of sample proportion for which we will reject the null hypothesis is

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Now it is given that p = 27 / 50= 0.54

The z-score for and p = 0.54 is

The power of the test is

power = P(z > 0.71) = 1 - P(z <= 0.71) = 1 - 0.7611 = 0.2389