Question

A Tim Horton's manager claims that more than 75% of customers purchase a coffee when they visit the store. We take a random sample of 225 customers and that 180 of them purchased a coffee. We would like to conduct a hypothesis test to determine whether there is significant evidence to support the manager's claim. The P-value for the appropriate hypothesis test is:

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.75

H_a : p >  0.75

n = 225

x = 180

= x / n = 180 / 225 = 0.8

P₀ = 0.75

1 - P₀ = 0.25

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.8 - 0.75 / [(0.75 * 0.25) / 225]

= 1.73

Test statistic = 1.73

P(z > 1.75) = 1 - P(z < 1.75) = 1 - 0.9599 = 0.0401

P-value = 0.0401

The P-value for the appropriate hypothesis test is 0.0401 .

= 0.05

P-value <

Reject the null hypothesis .

There sufficient evidence to that the significant evidence to support the manager's claim .