Question

1. Operating Costs of an Automobile (Population – Critical Value)

The average cost of owning and operating an automobile is $9122 per year. A random survey of 40 owners revealed an average cost of $9350 with a population standard deviation of $750. Is there sufficient evidence to conclude that the average is greater than $9122. Use α = 0.01.

Step 1: State the hypotheses.

Step 2: Find the critical value.

Step 3: Compute the test value.

Step 4: Make the decision.

Step 5: Summarize the results.

Answer 1

Step 1: State the hypotheses.

Ho:

Ha:

Step 2: Find the critical value.

z critical value is excel is

=NORM.INV(0.99;0;1)

=2.326347874

z crit at 99%=2.33

Step 3: Compute the test value

Z=xbar-mu/sigma/sqrt(n)

Z=(9350-9122)/(750/sqrt(40))

Z=1.922665

Step 4: Make the decision.

test statistic <critical value

Fail to reject null hypothesis.

Step 5: Summarize the results.

There is no sufficient evidence at 1% level of significance to conclude that  the average is greater than $9122