Question

Suppose the average commute time of your employees is unknown. The standard deviation of their commute time is estimated as 36.9 minutes.

How many employees must be included in a sample to create a 95 percent confidence interval for the average commute time with a confidence interval width of no more than 19 minutes?

Note that the correct answer will be evaluated based on the z-values in the summary table in the Teaching Materials section.

Remember to round your answer up to an integer.

Note that the correct answer will be evaluated based on the full-precision result you would obtain using Excel.

Suppose you are working for a regional residential natural gas utility. For a sample of 95 customer visits, the staff time per reported gas leak has a mean of 228 minutes and standard deviation 30 minutes. The VP of network maintenance hypothesizes that the average staff time devoted to reported gas leaks is 235 minutes.

At a 10 percent level of significance, what is the upper bound of the interval for determining whether to accept or reject the VP's hypothesis?

Note that the correct answer will be evaluated based on the z-values in the summary table in the Teaching Materials section.

Please round your answer to the nearest tenth.

Note that the correct answer will be evaluated based on the full-precision result you would obtain using Excel.

Answer 1

1)

given that

SD=36.9

Interval Width =19

since Interval width =2*Margin of error =2*E=19

this gives E=9.5

let the sample size is "n"

since Margin of error for 95% confidence level is given by

Hence n~58

2)

given that

sample mean =m=228

sample size =n=95

SD=30

for 10% level of significance upper bound of confidence interval is given by

since our upper bound is only 231.94 at 10% of level of significance that less than value of 235 hence these type of intervals does not contain the value of 235 hence we reject that mean is equal to 235.