Warren County Telephone Company claims in its annual report

Warren County Telephone Company claims in its annual report that “the typical customer spends $61 per month on local and long-distance service.” A sample of 12 subscribers revealed the following amounts spent last month.

$64 $64 $64 $68 $61 $64 $69 $65 $64 $66 $55 $68

A. What is the point estimate of the population mean? (Round your answer to 3 decimal places.)

B. Develop a 99% confidence interval for the population mean. (Use z Distribution Table.) (Round your answers to 3 decimal places.)

Solution

a)

The point estimate is the sample mean,

X = sample mean =    64.33333333   [ANSWER]

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b)         

Note that              
              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.005          
X = sample mean =    64.33333333          
z(alpha/2) = critical z for the confidence interval =    2.575829304          
s = sample standard deviation =    3.700941731          
n = sample size =    12          
              
Thus,              
              
Lower bound =    61.58139496          
Upper bound =    67.08527171          
              
Thus, the confidence interval is              
              
(   61.58139496   ,   67.08527171   ) [ANSWER]