Question

In a random sample of eight cell phones, the mean full retail price was $460.00 and the standard deviation was $173.00. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a 95% confidence interval for the population mean u. Interpret the results. Identify the margin of error. (Round to one decimal place as needed.) Construct a 95% confidence interval for the population mean. (Round to one decimal place as needed.) Interpret the results. Select the correct choice below and fill in the answer box to complete your choice (Type an integer or a decimal. Do not round.) O A. With % confidence, it can be said that the population mean full retail price of cell phones in dollars) is between the intervalls endpoints. OB. With % confidence, it can be said that most cell phones in the population have full retail prices (in dollars) that are between the interval's endpoints. OC. % of all random samples of eight people from the population of cell phones will have a mean full retail price in dollars) that is between the intervalls endpoints. OD. It can be said that % of the population of cell phones have full retail prices (in dollars) that are between the interval's endpoints.

Answer 1

sample mean, xbar = 460
sample standard deviation, s = 17
sample size, n = 8
degrees of freedom, df = n - 1 = 7

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.365

ME = tc * s/sqrt(n)
ME = 2.365 * 17/sqrt(8)
Margin of Error = 14.2

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (460 - 2.365 * 17/sqrt(8) , 460 + 2.365 * 17/sqrt(8))
CI = (445.8 , 474.2)

Option A) with 95% confidence