Homework Sourse1 Geoff is the proud owner of a restaurant Recently he read
1. 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 H0: ? = 24 and Ha: ? ? 24.
a)Calculate the P-value that corresponds to the sample and hypotheses. You may find this standard normal table useful. 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 ? = 0.05, Geoff should {C} acceptrejectnot reject the null hypothesis.
2.
Select whether a one-tailed or two-tailed hypothesis test is most appropriate in the following situations:
| One-tailed | Two-tailed | ||
|---|---|---|---|
| a) | A pharmacist wants to test whether the effect of a placebo is different from zero. | ![\"empty.gif\"](\"//www.perdisco.com/resources/image/global/empty.gif\") | |
| b) | A psychologist is interested in testing whether the mean I.Q. of all people is different from 100. | | |
| c) | The Roads and Traffic Authority wants to test whether the mean number of speeding fines on a particular road is greater than 10 per day. | | |
Solution
(1)(a) The test statisitc is
Z=(xbar-mu)/(s/vn)
=(22-24)/(7/sqrt(35))
=-1.69
It is a two-tailed test.
So the p-value=2*P(Z<-1.69)=0.0910 (from standard normal table)
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(b) Since the p-value is larger than 0.05, we do not reject the null hypothesis.
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(2)(a)Two-tailed
(b)Two-tailed
(c)One-tailed
