Geoff is the proud owner of a restaurant. Recently he read an article in Food We

Question

Geoff is the proud owner of a restaurant. Recently he read an article in Food Weekly which stated that the population mean preparation time for food at popular restaurants is equal to 24 minutes. A footnote at the bottom of the article said that the population standard deviation of preparation times was equal to 7 minutes. Geoff is interested in determining whether his restaurant has the same average preparation time as the popular restaurants described in the magazine article. Geoff timed how long it took to prepare 35 randomly selected meals over a week. The mean preparation time for the sample was calculated as 22 minutes. Geoff would like to use his sample to construct a hypothesis test with Ho: = 24 and Hai * 24. a) Calculate the P-value that corresponds to the sample and hypotheses. Give your answer as a decimal to 4 decimal places. P-value = b) Using the P-value for Geoff's hypothesis test and a level a = 0.01, Geoff should the null hypothesis.

Explanation / Answer

The statistical software output for this problem is:

One sample Z summary hypothesis test:
: Mean of population
H0 : = 24
HA : 24
Standard deviation = 7

Hypothesis test results:

Hence,

a) P - value = 0.0910

b) not reject

Mean n Sample Mean Std. Err. Z-Stat P-value 35 22 1.183216 -1.6903085 0.091

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