Question

5. A cellphone provider wants their subscribers to upgrade to a new cellphone with improved features. The provider will offer these new phones at a substantially reduced price in order to do this, however, unless at least 20% of the subscribers upgrade to the new phone, they will lose money with this offer. Data is collected from a random sample of 500 subscribers, and 135 of these subscribers indicate they would upgrade at the reduced price if offered.

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

            b. What would your decision be based on your conclusion in part a?

Answer 1

To test against

Here

sample proportion

and sample size

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 5% level of significance if P-value < 0.05

Now,

The value of the test statistic =

and P-value =

Since P-value < 0.05, so we reject H₀ at 5% level of significance and we can conclude that significantly more than 20% of the subscribers would upgrade to the new cellphone at the reduced price.