Question

Suppose the average time to complete a marathon is believed to be 264 minutes. If a random sample of 67 marathon runners posted an average time of 248 minutes, with a standard deviation of 46.6 minutes, is there evidence to support the claim that the average time is lower than originally thought? Perform a hypothesis test with significance level 0.01.

A. State the null hypothesis in symbols and in a complete sentence.

B. State the alternative hypothesis in symbols and in a complete sentence.

C. Calculate the test statistic.

D. Calculate the p-value.

E. State your conclusion in context of the research question.

F. If you changed the significance level to 0.05, would that change your conclusion? Explain!

Answer 1

We have given = 264 , x bar = 248 , s = 46.6 , n = 67 and = 0.01

Claim : The average time is lower than originally thought, that is   < 264

Here claim contains < sign hence it is our alternate hypothesis.

And null hypothesis is always of equality.

Hence

A. Null hypothesis : = 264

The average time to complete a marathon is believed to be 264 minutes.

B. Alternate hypothesis : < 264

The average time to complete a marathon is lower than 264 minutes.

c)

F) if we change alpha to = 0.05

Decision rule:

if P value then reject H0.

If P value > then fail to reject H0.

Here P value < hence we reject H0.

Hence it would not change your conclusion.