Warren County Telephone Company claims in its annual report that \"the typical c

Question

Warren County Telephone Company claims in its annual report that "the typical customer spends $60 per month on local and long-distance service." A sample of 12 subscribers revealed the following amounts spent last month. $65 $61 $67 $55 $62 $62 $63 $67 $56 $55 $61 $69 (a) What is the point estimate of the population mean? (Round your answer to 3 decimal places.) Population mean $ (b) Determine the 98% confidence interval for the population mean. (Round your answers to 2 decimal places.) Confidence interval $ and $ (c) Is the company's claim that the "typical customer" spends $60 per month reasonable? No Yes

Explanation / Answer

(a) Point estimate of population mean is given by sample mean

Mean = (65+61+.........+69)/12 = 61.917

(b) s (sample standard deviation) = 4.719

Since, sample size is less than 30, t-statistic will be used to find out confidence interval

CI = (mean - t(0.01,11)*s/sqrt(N) , mean + t(0.01,11)*s/sqrt(N))

substituting values from above, mean = 61.917, s = 4.719, N = 12, t(0.01,11) = 2.718

CI = (58.21 , 65.62)

(c) Yes, company's claim that the "typical customer" spends $60 per month is reasonable as it lies in 98% confidence interval estimate of population mean

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