Suppose the average time to co
Suppose the average time to complete a marathon is believed tobe 264 minutes. If a random sample of 67 marathon runners posted anaverage time of 248 minutes, with a standard deviation of 46.6minutes, is there evidence to support the claim that the averagetime is lower than originally thought? Perform a hypothesis testwith significance level 0.01.
A. State the null hypothesis in symbols and in a completesentence.
B. State the alternative hypothesis in symbols and in a completesentence.
C. Calculate the test statistic.
D. Calculate the p-value.
E. State your conclusion in context of the researchquestion.
F. If you changed the significance level to 0.05, would thatchange your conclusion? Explain!
Answer:
We have given 
= 264 , x bar = 248, s = 46.6 , n = 67 and 
= 0.01
Claim : The average time is lower thanoriginally thought, that is < 264
Here claim contains < sign hence it is our alternatehypothesis.
And null hypothesis is always of equality.
Hence
A. Null hypothesis : = 264
The average time to complete a marathon is believed to be 264minutes.
B. Alternate hypothesis : < 264
The average time to complete a marathon is lower than 264minutes.
c) 
F) if we change alpha to = 0.05
Decision rule:
if P value 
thenreject H0.
If P value > then fail toreject H0.
Here P value < hence we rejectH0.
Hence it would not change yourconclusion.
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