Question

In a random sample of eleven cell​ phones, the mean full retail price was 401.00 and the standard deviation was 166.00. 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.

1-Identify the margin of error.

2-Construct a 90​% confidence interval for the population mean.

Answer 1

Formula for margin of error(ME) for constructing confidence interval for the population mean :

confidence interval for the population mean =

Number of cell phones in the sample : sample size : n= 11

Sample mean :  mean full retail price =401.00

Sample standard deviation : s= 166.00

Sample Size : n	11
Degrees of freedom : n-1	10
Confidence Level :	90
=(100-90)/100	0.1
/2=(0.1/2)	0.05
	1.8125

Margin of Error for  90​% confidence interval for the population mean μ:

Margin of Error = 90.7172

90​% confidence interval for the population mean μ = = 401.00 90.7172 =(310.2828,491.7172)

90​% confidence interval for the population mean μ = (310.2828, 491.7172)