A cellphone provider has the business objective of wanting to estimate 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 500 subscribers. The results indicate that 135 of the subscribers would upgrade to a new cellphone at a reduced cost.

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?
b. How would the manager in charge of promotional programs concerning residential customers use the results in (a)?

a) There is evidence that more than 20% of the customers would upgrade to a new cellphone at a reduced cost

b) The manager in charge of promotional programs concerning residential customers will help the customers to upgrade their cellphones at a reduced cost.

Step-by-step explanation:

sample size, n = 500

The number of subscribers who would upgrade to a new cellphone at reduced cost, X = 135

Proportion of those that would upgrade to a new cellphone,

The null hypothesis is that  less than or equal to 20%( i.e. 0.2) of the customers would upgrade to a new cellphone at a reduced cost while the alternative hypothesis is that more than 20% would upgrade to a new cellphone at a reduced cost.

Null hypothesis,

Alternative hypothesis,

The test statistic can be calculated as thus:

To get the p - value for the test statistic:

Since the p - value is less than 0.05 significance level, the null hypothesis will be rejected. (i.e. more than 20% would upgrade to a new cellphone at a reduced cost.)