Answer to Question #193999 in Statistics and Probability for Alice

Question

The service manager of Appliance Universe has recorded the times for a simple random sample of 50 refrigerator service calls taken from last year’s service records. The sample mean and standard deviation were 25 minutes and 10 minutes, respectively. a. Construct and interpret the 95% confidence interval for the mean. b. It’s quite possible that the population of such times is strongly skewed in the positive direction—that is, some jobs, such as compressor replacement, might take 3 or 4 hours. If this were true, would the interval constructed in part (a) still be appropriate? Explain your answer

 

Answer 1

a.

$n = 50 \\ \bar{x}=25 \\ s= 10$

The confidence interval limits is:

$\bar{x}±t \times \frac{s}{\sqrt{n}}$

The critical value of t at 0.05 level of significance and d.f. = 50-1=49 is:

t=2.010

The 95% confidence interval for the mean is given by:

$25.0±2.010 \times \frac{10}{\sqrt{50}} \\ 25.0±2.843 \\ (22.157, 27.843)$

b. Yes.

Since we are using the sample mean of a sample of over 30 service calls, this sample will strongly approximate to the normal distribution which would account for the positively skewed effect.