Question

With a previous contractor, the mean time to repair a pothole was 3.2 days. A city councilman thinks that the new contractor’s mean time to repair a pothole is higher than 3.2 days. He randomly selects a sample of 12 pothole service calls and obtains the following times to repair (in days):

6.2            4.3         7.1          2.9          5.4              3.7         5.5        0.7             7.5         5.6           2.6          1.7

Is there enough evidence to support the councilman’s claim? (use   alpha = 0.05 level of significance)

Assume all conditions are satisfied for your chosen hypothesis test.

Show all the steps of an appropriate hypothesis test, including finding the P-value. (can I get an explanation for each step please A,B,C,D,E,F)

A.) What are the null and alternate hypotheses?

B.) What is the decision Rule?

C.)What is the test statistic?

D.) What is the decision?

E.) What does the decision infer?

F.) What is the estimated P-Value?

Answer 1

A. Here claim is that the new contractor’s mean time to repair a pothole is higher than 3.2 days

So hypothesis is vs

B. The t-critical value for a right-tailed test, for a significance level of ?=0.05 is

tc?=1.796

Graphically

So decision rule is if tstat>tcritical reject the null hypothesis

C. For the given data &

So test statistics is

D. As t statistics is greater than t critical we reject the null hypothesis

E. We have sufficient evidence to support the claim  that the new contractor’s mean time to repair a pothole is higher than 3.2 days.

F. P value using excel formula is TDIST(1.98,11,1)=