Question

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 the packaging 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

Can Mr. Rutter conclude that the mean weight of the bags is less than 50 pounds? Use the 0.01 significance level.

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

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

What is your decision regarding H₀?

Determine the p-value. (Round your answer to 4 decimal places.)

Answer 1

The statistical software output for this problem is:

One sample Z hypothesis test:
μ : Mean of variable
H₀ : μ = 50
H_A : μ < 50
Standard deviation = 3

Hypothesis test results:

Variable	n	Sample Mean	Std. Err.	Z-Stat	P-value
Data	10	48.18	0.9486833	-1.9184484	0.0275

Hence,

a) Decision Rule:

Reject Ho if z < -2.33

b) Test statistic = -1.92

Decision: Fail to reject Ho because test statistic is not less than critical value.

c) p - Value = 0.0275