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Chapter 9: Q. 65. (page 606)

Attitudes The Survey of Study Habits and Attitudes (SSHA) is a

psychological test with scores that range from 0to200.. The mean score for U.S. college students is115. A teacher suspects that older students have better attitudes toward school. She gives the SSHA to an SRS of 45students from the more than 1000students at her college who are at least 30years of age. The teacher wants to perform a test at the 伪=0.05significance level of

H0: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.

Short Answer

Expert verified

The required answer is:

Yes, the conditions are fulfilled.

Step by step solution

01

Given information

Hypothesized population mean 渭0=115

Sample size (n)=45

Level of significance (伪)=0.05

The null and alternative hypotheses are as follows:

H0:渭=115Ha:渭>115

02

The objective is to check whether the conditions required to perform the hypothesis test for the population mean are satisfied or not. 

The following conditions must be met before conducting a hypothesis test on 渭:

Simple random samples must be drawn from the population.

The sample size should be large, n>30and the population should be normally distributed.

Requirement check:

The 45-person sample was chosen using a simple random sampling technique.

The sample size exceeds 30people.

Therefore, both the required conditions are met.

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Most popular questions from this chapter

Watching grass grow The germination rate of seeds is defined as the proportion of seeds that sprout and grow when properly planted and watered. A certain variety of grass seed usually has a germination rate of 0.80. A company wants to see if spraying the seeds with a chemical that is known to increase germination rates in other species will increase the germination rate of this variety of grass. The company researchers spray a random sample of 400grass seeds with the chemical, and 339of the seeds germinate. Do these data provide convincing evidence at the 伪=0.05 significance level that the chemical is

effective for this variety of grass?

After once again losing a football game to the archrival, a college鈥檚 alumni association conducted a survey to see if alumni were in favor of firing the coach. An SRS of 100 alumni from the population of all living alumni was taken, and 64 of the alumni in the sample were in favor of firing the coach. Suppose you wish to see if a majority of all living alumni is in favor of firing the coach. The appropriate standardized test statistic is

(a)z=0.64-0.50.64(0.36)100z=0.64-0.50.64(0.36)100

role="math" localid="1654432946823" (b)t=0.64-0.50.64(0.36)100t=0.64-0.50.64(0.36)100

(c)z=0.64-0.50.5(0.5)100z=0.64-0.50.5(0.5)100

(d)z=0.64-0.50.64(0.36)64z=0.64-0.50.64(0.36)64

(e)z=0.5-0.640.5(0.5)100z=0.5-0.640.5(0.5)100

Restaurant power Refer to Exercise 86 Determine if each of the following changes would increase or decrease the power of the test. Explain your answers.

a. Use a random sample of 30 people instead of 50 people.

b. Try to detect that 渭=\(85,500 instead of 渭=\)86,000

c. Change the significance level to 伪=0.10

Awful accidents Slow response times by paramedics, firefighters, and policemen can have serious consequences for accident victims. In the case of life-threatening injuries, victims generally need medical attention within 8minutes of the accident. Several cities have begun to monitor emergency response times. In one such city, emergency personnel took more than 8minutes to arrive on 22%of all calls involving life-threatening injuries last year. The city manager shares this information and encourages these first responders to 鈥渄o better.鈥� After 6months, the city manager selects an SRS of 400 calls involving life- threatening injuries and examines the response times. She then performs a test at the 伪=0.05level of H0: p=0.22versus Ha:p<0.22, where pis the true proportion of calls involving life-threatening injuries during this 6-month period for which emergency personnel took more than 8minutes to arrive.

a. Describe a Type I error and a Type II error in this setting.

b. Which type of error is more serious in this case? Justify your answer.

c. Based on your answer to part (b), do you agree with the manager鈥檚 choice of 伪=0.05? Why or why not?

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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