Rutter Nursery Company packages its pine bark mulch in 50-pound bags. From a long history, the production department reports that the distribution of the bag weights follows the normal distribution and the standard deviation of this process is 3 pounds per bag. At the end of each day, Jeff Rutter, the production manager, weighs 10 bags and computes the mean weight of the sample. Below are the weights of 10 bags from today's production.

45.6

47.7

47.6

46.3

46.2

47.4

49.2

55.8

47.5

48.5

Click here for the Excel Data File

Can Mr. Rutter conclude that the mean weight of the bags is less than 50 pounds? Use the .01 significance level.

a.What is the decision rule?(Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

Reject H₀: 50 and fail to reject H₁: 50 when the test statistic is

(Click to select)

less than

greater than

equal to

.

b.The value of the test statistic is.(Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

c.What is your decision regarding H₀?(Click to select)

Fail to reject

Reject

, the mean weight

(Click to select)

is not

is

less than 50 pounds.

d.Determine thep-value.(Round your answer to 4 decimal places.)