Question

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 25% 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.

1. At the 0.05 level of significance, is there evidence that more than 25% of the subscribers would upgrade to the new cellphone at the reduced price? State your null and alternative hypothesis and justify your answer.
2. What would your decision be based on your conclusion in part a?

Answer 1

Solution-A:

Ho:p=0.25

Ha:p>0.25

alpha=0.05

calcualtion of test statistic

z=p^-p/sqrt(p*(1-p)/n)

p^=x/n=135/500=0.27

z=(0.27-0.25)/sqrt(0.25*(1-0.25)/500)

z= 1.032796

P value ine xcel is

=NORM.S.DIST( -1.032796,TRUE)

=0.150849688

p=0.1508

P>0.05

Fail to reject Ho

Accept Ho

Solution-b:

p=0.1508

P>0.05

Fail to reject Ho

Accept Ho

There is no suffcient statistical evidence at 5% level of significance to conclude that

more than 25% of the subscribers would upgrade to the new cellphone at the reduced price