A telephone company is trying to decide whether some new lines in a large commun

Question

A telephone company is trying to decide whether some new lines in a large community should be installed underground. Because a small surcharge will be added to telephone bills to pay for the extra installation costs, the company has decided to survey customers and proceed only if the survey strongly indicates that more than 60% of all customers favor underground installation. If 118 of 160 customers surveyed favor underground installation despite the surcharge, what should the company do? Test the relevant hypothesis using 0.05.

Explanation / Answer

Solution:

Hypothesis test for proportion:

H0:p=0.6

H1:p>0.6

alpha=0.05

Test statistic:

p^=x/n=118/160=0.7375

n=160

Z=p^-p/sqrt(p(1-p)/n

=0.7375-0.6/sqrt(0.6*(1-0.6)/160)

Z =3.55

p value=0.000193

p<0.05

Reject Null hypothesis

There is sufficient statistical evidence at 5% level of signiifcance to conlcude that more than 60% of all customers favour underground installation despite the surcharge.

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