The routes of postal deliverers are carefully planned so that each deliverer works between 7 and 7.5 hours per shift. The planned routes assume an average walking speed of 2 miles per hour and no shortcuts across lawns. In an experiment to examine the amount of time deliverers actually spend completing their shifts, a random sample of 75 postal deliverers was secretly timed. Calculate the mean for the variable of interest, report your answers with 2 decimals or with 4 for very small numbers.

Times

6.9

6.9

7.3

7.0

7.0

6.8

7.0

6.8

6.6

7.0

6.3

6.7

7.1

6.6

6.9

6.9

6.8

6.8

6.9

6.5

6.7

7.1

6.2

6.9

6.6

6.9

6.7

6.9

7.3

6.9

7.4

7.3

7.1

7.2

7.0

7.1

6.9

7.0

6.9

6.8

7.0

6.8

7.0

7.0

6.9

6.7

6.9

7.3

7.1

6.9

7.0

6.9

6.8

6.8

6.9

6.9

7.0

7.2

7.1

6.5

6.8

7.1

6.5

7.0

6.5

7.1

7.3

6.8

6.9

6.8

6.9

7.0

7.1

7.0

7.0

A)Compute the standard error for the variable times.

B)Construct a 95% confidence interval for the population mean (1). Report LB,UB.

C)Now, conduct a test and report the test statistics necessary to answer this question:

Is there enough evidence at the 1% significance level to conclude that postal workers are on average spending less than 7 hours per day doing their jobs?

D)Report the p-value for this test, Reject or not reject the null hypothesis?

E)Explain if there is enough evidence at the 1% significance level to conclude that postal workers are on average spending less than 7 hours per day doing their jobs?

How does this conclusion compare to the confidence interval that you calculated at the 95% level?