Question

The number of cars sold annually by used car salespeople is normally distributed with a standard deviation of 15. A random sample of 390 salespeople was taken and the mean number of cars sold annually was found to be 77. Find the 91% confidence interval estimate of the population mean.

Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits.

Confidence Interval =

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 77

sample standard deviation = s = 15

sample size = n = 390

Degrees of freedom = df = n - 1 = 390-1 =389

At 91% confidence level

= 1-0.91% =1-0.91 =0.09

/2 =0.09/ 2= 0.045

t/2,df = t_{0.045,389 = 1.700}

t _/2,df = 1.700

Margin of error = E = t_/2,df * (s /n)

=1.700 * (15 / 390)

Margin of error = E = 1.291

The 91% confidence interval estimate of the population mean is,

- E < <  + E

77 - 1.291< < 77+ 1.291

75.709 < < 78.291

(75.709, 78.291 )

Lower limit = 75.709

Upper limit = 78.291