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Chapter 9: 56 (page 564)

Reporting cheating What proportion of students

are willing to report cheating by other students? A

student project put this question to an SRS of 172

undergraduates at a large university: 鈥淵ou witness two

students cheating on a quiz. Do you go to the professor?鈥�

The Minitab output below shows the results of a

significance test and a 95% confidence interval based

on the survey data.18

(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 in context.

(d) Do these data give convincing evidence that the actual population proportion differs from 0.15? Justify your answer with appropriate evidence.

Short Answer

Expert verified

Part (a) Population proportion

Part (b) If p-value is less than 0.05 implies the test is significant.

Part (c) 0.146>0.05, Test is not significant.

Part (d) No conclusion can be drawn

Step by step solution

01

Part (a) Step 1. Parameter of interest

The Minitab output represents the confidence interval of the population proportion. So, the parameter of interest is the population proportion.

02

Part (b) Step 1. Decision Criteria 

The criteria for testing whether the hypothesis test is significant or not. In other words, if the probability of rejecting the null hypothesis is less than 0.05 implies that the test is significant.

03

Part (c) Step 1. Interpretation

It can be observed that the p-value is less than 0.05, that is,

0.146>0.05

As a result, the test is insignificant as there is not enough evidence to reject the null hypothesis.

04

Part (d)  Step 1 Conclusion 

It can be observed that there is not enough evidence to reject the null hypothesis and the test is not significant. So, no conclusion can be made about the claim.

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Most popular questions from this chapter

Attitudes The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students鈥� attitudes toward school and study habits. Scores range from 0to200. The mean score for U.S. college students is about 115. A teacher suspects that

older students have better attitudes toward school. She gives the SSHA to an SRS of 45of the over 1000students at her college who are at least 30years of age. Check the conditions for carrying out a significance test of the teacher鈥檚 suspicion.

A Gallup Poll report on a national survey of 1028 teenagers revealed that 72% of teens said they seldom or never argue with their friends. Yvonne wonders whether this national result would be true in her large high school. So she surveys a

a random sample of 150 students at her school.

A researcher plans to conduct a significance test at the 伪=0.01significance level. She designs her study to have a power of 0.90 at a particular alternative value of the parameter of interest. The probability that the researcher will commit a Type Il error for the particular alternative value of the parameter at which she computed the power is

(a) 0.01

(b) 0.10

(c) 0.89

(d) 0.90

(c) 0.99

A 95%confidence interval for a population mean is calculated to be (1.7,3.5). Assume that the conditions for performing inference are met. What conclusion can we draw for a test of role="math" localid="1650275427722" H0:渭=2versus Ha:渭鈮�2at the A=0.05level based on the confidence interval?

(a) None. We cannot carry out the test without the original data.

(b) None. We cannot draw a conclusion at the A=0.05level since this test is connected to the 97.5%confidence interval.

(c) None. Confidence intervals and significance tests are unrelated procedures.

(d) We would reject H0at level A=0.05.

(e) We would fail to reject H0at level A=0.05.

Stating hypotheses State the appropriate null and alternative hypotheses in each of the following cases.

(a) The average height of 18-year-old American women is 64.2inches. You wonder whether the mean height of this year's female graduates from a large local high school (over 3000students) differs from the national average. You measure an SRS of 48female graduates and find that X=63.1inches.

(b) Mr. Starnes 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 students at the school to help Mr. Starnes test his claim.

- Check conditions for carrying out a test about a population proportion or mean.

- Interpret P-values in context.
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