Question

In: Statistics and Probability

The number of cars sold annually by used car salespeople is normally distributed with a standard...

The number of cars sold annually by used car salespeople is normally distributed with a standard deviation of σ = 15. A random sample of 36 salespeople was taken and the mean number of cars sold annually was found to be 141. Find the 99% 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.

(a) [3 pts] What process of finding confidence interval you would choose and why?

(b) [4 pts] Find the margin of error:

(c) [4 pts] Find the confidence interval:

(d) [4 pts] Interpret the confidence Interval:

Solutions

Expert Solution

Solution :

Given that,

a)Single-Sample Confidence Interval Using the Z Statistic, because is known .



Point estimate = sample mean = = 141


Population standard deviation = = 15

Sample size = n = 36

At 99% confidence level

= 1-0.99% =1-0.99 =0.01

/2 =0.01/ 2= 0.005

Z/2 = Z0.005 = 2.576

Z/2 = 2.576

b) Margin of error = E = Z/2 * ( /n)

= 2.576 * ( 15 /  36 )

= 6.44

c) At 99 % confidence interval estimate of the population mean is,

- E < < + E

141 - 6.44 <   < 141+ 6.44

134.56 <   < 147.44

(134.56 , 147.44)

Lower confidence interval =134.56

Upper confidence interval=147.44

D) The 99% confidence interval estimate of the population mean is =(134.56 , 147.44)

orchestra answered 2 years ago
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