I need help finding the answer to this question. It has had me stuck at the poin

Question

I need help finding the answer to this question. It has had me stuck at the point where I am calculating the value of the test statistic for a while now.

A telephone company estimates that 30% of its customers are interested in high-speed internet services. To test this estimate, a random sample of 100 customers was selected and the results showed that 25 were interested in high-speed internet service. Can it be concluded that the percentage of customers interested on high-speed internet service is different from 30%? Formulate and test the appropriate hypotheses at a 5% significance level. Use the critical value approach.

Explanation / Answer

Given n=100, p=25/100=0.25

The test hypothesis is
Ho:p =0.3
Ha:p not equal to 0.3

The test statistic is
Z=(0.25-0.3)/[0.3*0.7/100]

=-1.09

Given a=0.05, the critical value is Z(0.025)=-1.96(check standard normal table)

Since Z=-1.09>-1.96, we do not reject Ho.

So we can not conclude that the percentage of customers interested in high-speed internet service is different from 30%

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