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Chapter 9: Q .8. (page 564)

Stating hypotheses

a. A change is made that should improve student satisfaction with the parking situation at your school. Before the change, 37%of students approve of the parking that's provided. The null hypothesis H0:p鈭�=0.37H0:p^=0.37is tested against the alternative Ha: p鈭�>0.37Ha:p^>0.37

b. A researcher suspects that the mean birth weights of babies whose mothers did not see a doctor before delivery is less than 3000 grams. The researcher states the hypotheses as

H0:渭=3000gramsH0:渭=3000grams

Ha:渭鈮�2999gramsHa:渭鈮�2999grams

Short Answer

Expert verified

The appropriate hypotheses are:

Part (a)H0:p=0.37,Ha:p>0.37

Part (b)H1:p>0.50,Ha:渭<3000

Step by step solution

01

Part (a)Step 1:Given information

H0:渭=3000gramsH0:渭=3000grams

Ha:渭鈮�2999gramsHa:渭鈮�2999grams

02

Part (a) Step 2:Explaination

Inequalities are shown in the null hypothesis not the alternative hypothesis. Here, inequality has been provided in the alternative hypothesis and value of the parameter must be same in both the parameters. So, it is required to replace 2999 by 3000

The hypotheses are:

H0:渭=3000Ha:渭<3000

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Most popular questions from this chapter

Side effects A drug manufacturer claims that less than 10%of patients who take its new drug for treating Alzheimer鈥檚 disease will experience nausea. To test this claim, researchers conduct an experiment. They give the new drug to a random sample of 300out of 5000Alzheimer鈥檚 patients whose families have given informed consent for the patients to participate in the study. In all, 25of the subjects experience nausea.

a. Describe a Type I error and a Type II error in this setting, and give a possible

consequence of each.

b. Do these data provide convincing evidence for the drug manufacturer鈥檚 claim?

Restaurant power Refer to Exercise 86 Determine if each of the following changes would increase or decrease the power of the test. Explain your answers.

a. Use a random sample of 30 people instead of 50 people.

b. Try to detect that 渭=\(85,500 instead of 渭=\)86,000

c. Change the significance level to 伪=0.10

Teens and sex The Gallup Youth Survey asked a random sample of U.S. teens aged 13 to 17 whether they thought that young people should wait until marriage to have sex.14 The Minitab output shows the results of a significance test and a 95% confidence interval based on the survey data.

a. Define the parameter of interest.

b. Check that the conditions for performing the significance test are met in this case.

c. Interpret the P-value.

d. Do these data give convincing evidence that the actual population proportion differs from 0.5? Justify your answer with appropriate evidence.

18%Members of the city council want to know if a majority of city residents supports a 1%increase in the sales tax to fund road repairs. To investigate, they survey a random sample of 300city residents and use the results to test the following hypotheses:

H0:p=0.50

Ha:p>0.50

where pis the proportion of all city residents who support a 1%increase in the sales tax to fund road repairs.

In the sample, p^=158/300=0.527, The resulting P-value is 0.18. What is the correct interpretation of this P-value?

a. Only 18% of the city residents support the tax increase.

b. There is an 18%chance that the majority of residents supports the tax increase.

c. Assuming that 50%of residents support the tax increase, there is an 18%probability that the sample proportion would be 0.527or greater by chance alone.

d. Assuming that more than 50%of residents support the tax increase, there is an 18%probability that the sample proportion would be 0.527or greater by chance alone.

e. Assuming that 50%of residents support the tax increase, there is an 18% chance that the null hypothesis is true by chance alone.

Error probabilities and power You read that a significance test at the 伪=0.01

significance level has probability 0.14of making a Type II error when a specific alternative is true.

a. What is the power of the test against this alternative?

b. What鈥檚 the probability of making a Type I error?
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