Question

According to the University of Nevada Center for Logistics Management, 9% of all merchandise sold in the United States gets returned. A Houston department store sampled 90 items sold in January and found that 15 of the items were returned.

c. Is the proportion of returns at the Houston store significantly different from the returns for the nation as a whole? Provide statistical support for your answer.

z - value is 2.54

What is the p-value?

Answer 1

Solution :

Given that,

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.09

H_a : p 0.09

n = 90

x = 15

= x / n = 15 / 90 = 0.1667

P₀ = 0.09

1 - P₀ = 1 - 0.09 = 0.91

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.1667 - 0.09 / [(0.09 * 0.91) / 90 ]

= 2.54

Test statistic = 2.54

P(z > 2.54) = 1 - P(z < 2.54) = 1 - 0.9945 = 0.0055

P-value = 0.0055