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 97 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. Complete parts​ (a) and​ (b) below. 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? Determine the null​ hypothesis What is the test​ statistic? Upper Z Subscript STATequals nothing ​(Type an integer or a decimal. Round to two decimal places as​ needed.) What is the​ p-value? The​ p-value is nothing. ​(Type an integer or a decimal. Round to three decimal places as​ needed.) What is the final​ conclusion? ▼ Do not/ reject Reject the null hypothesis. There ▼ is/ is not sufficient evidence that the percentage of people who would upgrade to a new cellphone at a reduced cost is ▼ greater than/ less than different from 20​%. b. How would the manager in charge of promotional programs concerning cellphone upgrades use the results in​ (a)? The manager ▼ should/should not suggest reducing the price.

Answer 1

H0: p = 0.20
Ha: p > 0.20

pcap = 97/400 = 0.2425

Standard deviation
SE = sqrt(p*(1-p)/n)
SE = sqrt(0.2 * 0.8 / 400)
SE = 0.02

Test statistic,
z = (pcap - p)/SE
z = (0.2425 - 0.2)/0.02
z = 2.13

p-value = P(z > 2.13) = 0.017
Reject H0
There is sufficient evidence that the percentage of people who would upgrade to a new cellphone at a reduced cost is greater than from 20​%

b)
The manager should suggest reducing the price.