Question

[3] In a random sample of 13 cell phones, the mean full retail price was $745 with standard deviation of $152. Assume the population is normally distributed. Find the margin of error and the 95% confidence interval for the population mean.

Answer 1

SOLUTION:

From given data,

In a random sample of 13 cell phones, the mean full retail price was $745 with standard deviation of $152. Assume the population is normally distributed. Find the margin of error and the 95% confidence interval for the population mean.

Sample size = n = 13

Mean = = 745

Standard deviation = s = 152

95% confidence interval

95% = 95/100 = 0.95

= 1-0.95 = 0.05

/2 = 0.05/2 = 0.025

Degree of freedom :

df = n-1 = 13-1 = 12

Critical value:

t_/2,df = t_0.025,12 = 2.178812

Margin of error (E) :

E = t_/2,df * (s/sqrt(n))

E = 2.178812 * (152/sqrt(13))

Margin of error = E = 91.85

The 95% confidence interval for the population mean

Formula :

E

- E <   < + E

745 - 91.85 <   < 745 + 91.85

653.15 <   < 836.85