Are people moving away from having a traditional land line telephone in their ho

Question

Are people moving away from having a traditional land line telephone in their homes? A random sample of 153 people was asked "Do you have a traditional telephone in your place of residence?" Of those asked, 95 said they do have a traditional telephone.

1. The 95% confidence interval estimate is:

a) (0.544, 0.698)

b) (0.520, 0.722)

c) (0.617, 0.625)

d) (0.278, 0.480)

2. How large a sample n would you need to estimate p with a margin of error of 0.03 with 99% confidence? Use the approximation the p=0.5 as the value for p in your calculation.

a) n=33

b) n=153

c) n=1068

d) n=1844

how do you solve this?

Explanation / Answer

1) it is option c) (0.544,0.698)

working :

p- z(alpha/2)*sqrt((p)*(1-p)/n) <= p <= p+z(alpha/2)*sqrt((p)*(1-p)/n)

here z(alpha/2)=1.96

2) using the same formula , we get n = 1844

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