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Chapter 9: Q 48. (page 582)

Proposition XA political organization wants to determine if there is convincing evidence that a majority of registered voters in a large city favor Proposition X. In an SRS of 1000registered voters, 482favor the proposition. Explain why it isn鈥檛 necessary to carry out a significance test in this setting.

Short Answer

Expert verified

Sample proportion is less than0.5

Step by step solution

01

Given Information

It is given that n=1000

x=482

Claim is greater than50%

02

Explanation and Calculation

As per given data:

Null Hypothesis: H0:p=50%=0.5

Alternative Hypothesis: H1:p>0.5

Sample proportion is calculated as:

p^=xn=4821000=0.485

Claim is population proportion less than 0.5. Sample proportion after calculation is less than 0.5.

So, there is no proof given by sample proportion that alternative hypothesis could be true.

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Most popular questions from this chapter

How much juice? Refer to Exercises 3 and 11 .

a. What conclusion would you make at the 伪=0.10伪=0.10level?

b. Would your conclusion from part (a) change if a 5 \% significance level was used instead? Explain your reasoning.

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.

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?

You are thinking of conducting a one-sample ttest about a population mean 渭using a 0.05significance level. Which of the following statements is correct?

a. You should not carry out the test if the sample does not have a Normal distribution.

b. You can safely carry out the test if there are no outliers, regardless of the sample size.

c. You can carry out the test if a graph of the data shows no strong skewness, regardless of the sample size.

d. You can carry out the test only if the population standard deviation is known.

e. You can safely carry out the test if your sample size is at least 30 .

No homework? Mr. Tabor believes that less than 75%of the students at his school completed their math homework last night. The math teachers inspect the homework assignments from a random sample of 50 students at the school.
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