Question

A delivery truck manager takes a sample of 25 delivery trucks and calculates the sample mean and sample standard deviation for the cost of operation. A 95% confidence interval for the population mean cost is constructed and found to be $253 to $320. He reasons that this interval contains the mean operating cost for the entire fleet of delivery trucks since the sample mean is contained in this interval.

Required:
a. Do you agree with his reasoning?
b. How would you interpret this confidence interval?
c. Is this an appropriate use of a confidence interval?
d. Concerning your answers to parts a through c, what assumptions did you make (if any)? Does the Central Limit Theorem apply? Why or why not?
e. How does this apply or could apply to your profession?

Answer 1

a) No.

b) Lies between 253 and 320.

c) No.

d) Central limit theorem is not applicable here.

e) The process of estimation can always help us make the right prediction about future sales, demands, costs, profits, and so on based on the past data or any such data available and hence take the correct decision

Explanation:

1) No I do not agree, it's just because the mean should be always within the confidence interval. in this case, the above statement doesn't satisfy the condition.

2)The true mean values at 95% confidence interval lies between 253 and 320.

3) No, because this is only used for the difference in mean. If there is a difference then the mean is different.

4) Central limit theorem is not applicable here. Since the sample size is very small, it better to use t distribution rather which indicated normal data.

in case the sample size is greater than 30, we can then apply the central limit theorem.

5) The process of estimation can always help us make the right prediction about future sales, demands, costs, profits, and so on based on the past data or any such data available and hence take the correct decision.