The routes of postal deliverers have been 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 time deliverers actually spend completing their shifts, a random sample of 75 postal deliverers was secretly timed. USE R code to solve this question. Please post the code as well.

Calculate the mean for the variable of interest,

Compute the standard error for the variable times.

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

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

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?

Report the p-value for this test.

Reject or not reject the null hypothesis?

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