Warren County Telephone Company claims in its annual report that “the typical cu
ID: 3324893 • Letter: W
Question
Warren County Telephone Company claims in its annual report that “the typical customer spends $63 per month on local and long-distance service.” A sample of 12 subscribers revealed the following amounts spent last month. $63 $64 $63 $67 $58 $64 $69 $62 $64 $67 $54 $68 a. What is the point estimate of the population mean? (Round your answer to 3 decimal places.) Estimated population mean $ b. Develop a 90% confidence interval for the population mean. (Use t Distribution Table.) (Round your answers to 3 decimal places.) Confidence interval for the population mean $ and $ c. Is the company's claim that the "typical customer" spends $63 per month reasonable?
Explanation / Answer
A) Point estimate of the population mean = (63 + 64 + 63 + 67 + 58 + 64 + 69 + 62 + 64 + 67 + 54 + 68)/12 = 63.58
Standard deviation (S) = 4.25
B) DF = 12 - 1 = 11
With 11 degrees of freedom and 90% confidence interval the critical value is 1.796
The confidence interval is
Mean +/- t0.05, 11 * SD /sqrt (n )
= 63.58 +/- 1.796 * 4.25/sqrt(12)
= 63.58 +/- 2.203
= 61.377, 65.783
C) As the mean value 63 lies between the confidence interval, so the company's claim that the typical customer spends $63 per month is reasonable.
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