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Chapter 9: Q .15. (page 564)

pg559¯

No homework Refer to Exercises 1 and 9. What conclusion would you make at theα=0.05α=0.05level?

Short Answer

Expert verified

There is not enough convincing evidence to help the claim that less than75%of the students at researcher's school finished their homework last night.

Step by step solution

01

Step 1:Given information

α=0.05andα=0.05

02

Step 2:Explaination

P=0.1265=12.65%

α=0.05

Given claim is proportion is less than 75%

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis statement is 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.

H0:p=75%=0.75

Ha:p<0.75

If the P-value is smaller than the significance level α, then reject the null hypothesis:

0.1265>0.05⇒Fail to rejectH0

There is not enough convincing evidence to help the claim that less than75% of the students at researcher's school finished their homework last night.

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Most popular questions from this chapter

Don’t argue Refer to Exercises 2 and 12.

a. What conclusion would you make at the α=0.01 level?

b. Would your conclusion from part (a) change if a 5% significance level was used

instead? Explain your reasoning.

Interpreting a P-value A student performs a test of H0:p=0.3H0:p=0.3versus Ha:p<0.3Ha:p<0.3and gets a P-value of 0.22The student says, "This means there is about a22%chance that the null hypothesis is true." Explain why the student's explanation is wrong.

More lefties?In the population of people in the United States, about 10% are left-handed. After bumping elbows at lunch with several left-handed students, Simon wondered if more than 10%of students at his school are left-handed. To investigate, he selected an SRS of 50students and found 8lefties (p⏜=8/50=0.16).

To determine if these data provide convincing evidence that more than 10%of the students at Simon’s school are left-handed, 200trials of a simulation were conducted. Each dot in the graph shows the proportion of students that are left-handed in a random sample of 50students, assuming that each student has a 10%chance of being left handed.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest.

b. Use the simulation results to estimate the P-value of the test in part (a). Interpret the P-value.

c. What conclusion would you make?

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

A95%confidence interval for the proportion of viewers of a certain reality television

show who are over 30 years old is (0.26,0.35). Suppose the show's producers want to est the hypothesis \H0:p=0.25against Ha: Ha:p≠0.25. Which of the following is an appropriate conclusion for them to draw at the α=0.05

a. Fail to reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old equals 0.25

b. Fail to reject H0there is not convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from0.25.

c. Reject H0; there is not convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from 0.25

. d. Reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old is greater than 0.25.

e. Reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from0.25.
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