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Chapter 9: Q 35. (page 581)

Home computers Jason reads a report that says 80%of U.S. high school

students have a computer at home. He believes the proportion is smaller than 0.80at his large rural high school. Jason chooses an SRS of 60students and finds that 41have a computer at home. He would like to carry out a test at the α=0.05significance level of H0:p=0.80versus Ha:p<0.80, where p= the true

proportion of all students at Jason’s high school who have a computer at home. Check if the conditions for performing the significance test are met.

Short Answer

Expert verified

Yes, the conditions are fulfilled.

Step by step solution

01

Given Information

It is given that
(n)is60

(p)is0.80

H0:p=0.80

Ha:p<0.80

02

Checking the conditions

prefers to the proportion of students that own computer at home.

Conducting significance test, below conditions should be satisfied.

n×p≥10

n×(1-p)≥10

(1) n×p=60×0.8

=48>10

(2) n×(1-p)=60×(1-0.80)

=12>10

Both conditions are satisfied.

So, we can conduct significance test.

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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’s 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’s 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’s claim?

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∧=0.37H0:p^=0.37is tested against the alternative Ha: p∧>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:μ=3000gramsH0:μ=3000grams

Ha:μ≤2999gramsHa:μ≤2999grams

Better parking A local high school makes a change that should improve student satisfaction with the parking situation. Before the change, 37% of the school’s students approved of the parking that was provided. After the change, the principal surveys an SRS of students at the school. She would like to perform a test of H0:p=0.37Ha:p>0.37where p is the true proportion of students at school who are satisfied with the parking

situation after the change.

a. The power of the test to detect that p=0.45 based on a random sample of 200 students and a significance level of α=0.05 is 0.75 Interpret this value.

b. Find the probability of a Type I error and the probability of a Type II error for the test in part (a).

c. Describe two ways to increase the power of the test in part (a).

You are thinking of conducting a one-sample ttest about a population mean μusing 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 .

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’t necessary to carry out a significance test in this setting.
See all solutions

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