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Chapter 9: Q .1. (page 563)

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.

Short Answer

Expert verified

H0:p=75%=0.75

Ha:p<0.75

Step by step solution

01

Step 1:Given information

Claim is proportion is less than 75%

02

Step 2:Explaination

The null hypothesis statement is that the population is equal to the value mentioned in the claim:

H0:p=75%=0.75

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis states that the population proportion is equal to the value given in the claim. If the null hypothesis is the claim,

then the alternative hypothesis statement is the opposite of the null hypothesis.

Ha:p<0.75

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Most popular questions from this chapter

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 200from the more than 2500students at the school. In all, 83students say that they approve of the new parking arrangement. The principal cites this as evidence that the change was effective.

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

consequence of each.

b. Is there convincing evidence that the principal’s claim is true?

The standardized test statistic for a test of H0:p=0.4versus Ha:pnotequalto0.4isz=2.43This test is

a. not significant at either α=0.05or α=0.01

b. significant at α=0.05but not atα=0.01

c. significant atα=0.01but not at α=0.05

d. significant at both α=0.05andα=0.01

e. inconclusive because we don’t know the value of p^

Explaining confidence: Here is an explanation from a newspaper concerning one of its opinion polls. Explain what is wrong with the following statement.

For a poll of 1600 adults, the variation due to sampling error is no more than 3

percentage points either way. The error margin is said to be valid at the 95%

confidence level. This means that, if the same questions were repeated in 20 polls, the results of at least 19 surveys would be within 3 percentage points of the results of this survey.

Error probabilities and power You read that a significance test at the α=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’s the probability of making a Type I error?

Which of the following 95%confidence intervals would lead us to reject H0:p=0.30in favor of Ha:pnotequalto0.30at the 5%significance level?

a. (0.19,0.27)

b.(0.24,0.30)

c. (0.27,0.31)

d. (0.29,0.31)

e. None of these
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