Question

in a random sample of seven cell phones, the mean full retail price was $463.00 and the standard deviation was $222.00. assume the population is normally distributed and use the t - distribution to find the margin of error and construct a 90% confidence interval for the population mean μ. interpret the results.

identify the margin of error.

163.0 dollars
(round to one decimal place as needed.)

construct a 90% confidence interval for the population mean.

(, )
(round to one decimal place as needed.)

Explanation:

Step1: Recall the confidence interval formula

The formula for a confidence interval using the t - distribution is \(\bar{x}\pm E\), where \(\bar{x}\) is the sample mean and \(E\) is the margin of error. We are given \(\bar{x} = 463\) and \(E=163.0\).

Step2: Calculate the lower and upper bounds

For the lower bound: \(463 - 163.0=299.0\)
For the upper bound: \(463+163.0 = 626.0\)

Answer:

\((299.0,626.0)\)