what is the test statistic here? Zstat = ?

Question

A cellphone provider has the business objective of wanting to determine the proportion of subscribers who would upgrade to a new cellphone with improved features if it were made available at a substantially reduced cost. Data are collected from a random sample of 400 subscribers. The results indicate that 99 of the subscribers would upgrade to a new cellphone at a reduced cost. Reducing the price will be profitable if at least 20% of the subscribers would upgrade.

A. At the 0.05 level of significance, is there evidence that more than 20% of the customers would upgrade to a new cellphone at a reduced cost?

WHAT IS THE TEST STATISTIC HERE?

Answer 1

p = 0.20

phat = 99/400 = 0.2475

n = 400

Ho: p = 0.2

Ha: p > 0.2

this is a right tailed test

z = (phat - p)/sqrt(p * (1-p)/n) = (0.2475 - 0.2)/sqrt(0.2 * 0.8/400) = 0.75

at 0.05 significance level, critical z-value for right tailed test is 1.645.

since z-statistic is < 1.645, there is not sufficient evidence that the customers would upgrade to the new cellphone at a reduced cost.