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.

Question 1 (2 points)

The 99% confidence interval estimate for p is:

Question 1 options:

A)

(0.520, 0.722).

B)

(0.617, 0.625).

C)

(0.278, 0.480).

D)

(0.544, 0.698).

Question 2

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

Question 2 options:

A)

n = 1844

B)

n = 1068

C)

n = 153

D)

n = 33

A)

(0.520, 0.722).

B)

(0.617, 0.625).

C)

(0.278, 0.480).

D)

(0.544, 0.698).

Explanation / Answer

Q1.

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.620915033          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.039222805          
              
Now, for the critical z,              
alpha/2 =   0.005          
Thus, z(alpha/2) =    2.575829304          
Thus,              
              
lower bound = p^ - z(alpha/2) * sp =   0.519883781          
upper bound = p^ + z(alpha/2) * sp =    0.721946284          
              
Thus, the confidence interval is              
              
(   0.519883781   ,   0.721946284   )

or (0.520, 0.722) [OPTION A]

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