The manager of a local home inspection company claims that their agents conduct a mean of no more than 55 in-depth home surveys every week. The employees believe their manager is underestimating their workload to avoid paying overtime. The numbers of in-depth surveys conducted during a week by a random sample of agents are as follows:

55566158555054535863

At the 0.01 level of significance, can the employees prove they are actually conducting more than 55 surveys per week?

STEP 1: State the null and alternate hypotheses.

H₀:Answer

55 surveys per week > 55 surveys per week 55 surveys per week < 55 surveys per week 55 surveys per week

H₁:Answer

55 surveys per week 55 surveys per week 55 surveys per week = 55 surveys per week> 55 surveys per week < 55 surveys per week

This is a_____test.

STEP 2: State the level of significance.

=Answer

STEP 3: Identify the test statistic.

Answer

zt

STEP 4: Formulate a decision rule.

Reject H₀ifAnswer

ztAnswer

>

.

STEP 5: Take a sample, arrive at decision (complete calculation for test statistic).

Value of the sample mean:Answer

surveys per week

Value of the sample standard deviation:Answer

surveys per week

Value of test statistic:Answer

Therefore, we mustAnswer

not rejectrejectthe null hypothesis.

STEP 6: Interpret the result.

Based on sample data, evidence suggests that it isAnswer

likelynot likelythe employees are correct.The mean number of surveys conducted by the agentsAnswer

isis notactuallymore than 55 per week.