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Chapter 9: Q. 63 (page 587)

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.

Short Answer

Expert verified

The teacher selected an SRS of 45students. 10%:45is less than 10%of the population size of 1000. Normal/Large Sample: n=45鈮�30

Step by step solution

01

Given information

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 of45of the over 1000students at her college who are at least 30years of age.

02

Explanation

The teacher wants to perform a test at the 伪=0.05 significance level of

HO:渭=115Ha:渭>115

where 渭=the mean SSHA score in the population of students at her college who are at least 30years old. Check if the conditions for performing the test are met.

The teacher selected an SRS of 45students.

10%:45is less than 10%of the population size of 1000.

Normal/Large Sample:n=45>30

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Most popular questions from this chapter

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.

Ancient air The composition of the earth鈥檚 atmosphere may have changed over time. To try to discover the nature of the atmosphere long ago, we can examine the gas in bubbles inside ancient amber. Amber is tree resin that has hardened and been trapped in rocks. The gas in bubbles within amber should be a sample of the atmosphere at the time the amber was formed. Measurements on 9specimens of amber from the late Cretaceous era (75to95 million years ago) give these percents of nitrogen:

63.465.064.463.354.864.560.849.151.0Explain why we should not carry out a one-sample t test in this setting.

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 to have sex until marriage.17 The Minitab output below 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 in context.

(d) Do these data give convincing evidence that the actual population proportion differs from 0.5? Justify your answer with appropriate evidence.

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.

Sweetening colas Cola makers test new recipes for loss of sweetness during storage. Trained tasters rate the sweetness before and after storage. From experience, the population distribution of sweetness losses will be close to Normal. Here are the sweetness losses (sweetness before storage minus sweetness after storage) found by tasters from a random sample of 10batches of a new cola recipe:

2.00.40.72.0-0.42.2-1.31.21.12.3

Are these data good evidence that the cola lost sweetness? Carry out a test to help you answer this question.
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