Question 1199239: It takes runners on average 289 minutes to run the marathon. Drink
ZXZ manufacturer claims that drinking ZXZ helps runners to run the marathon
faster. To test that claim, we took 30 runners, and gave them to drink ZXZ before
they ran the marathon. In our sample, the average time to run the marathon was
281 minutes and the standard deviation of the times to run the marathon was 26
minutes.
Part a) What is H0 and what is H1 in this test?
Part b) Do we have enough evidence to reject H0 and accept H1?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! mean before drinking producct = 289 minutes.
mean after drinking product = 281 minutes
sample size is 30
sample mean = 281 minutes
sample standard deviation = 26 minutes
standard error = sample standard deviation / square root of sample size = 26 / sqrt(30) = 4.7469 rounded to 4 decimal places.
t-score = (281 - 289) / 4.7469 = -1.685 rounded to 3 decimal places.
area to the left of that t-score with 29 degrees of freedom = .0514 rounded to 4 decimal places.
H0 = mean of 289 minutes.
H1 = mean of 281 minutes
test is for H1 < H0, i.e. drinking product is supposed to reduce the amount of time it takes to run the marathon.
test alpha is equal to .0514 rounded to 4 decimal places.
at 95% one sided confidence interval, the critical alpha is .05.
the test alpha is higher than .05.
the conclusion is that there is not enough evidence to support the claim that drinking the product results in lower average times to complete the marathon at 95% confidence interval or higher.
if the confidence interval was less than 95%, it is possible that the test would have been significant and that the conclusion would have been that the test supported the conclusion that the average times were lower after drinking the product.
since you did not specify the required confidence interval, the results are inconclusive.
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