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Chapter 9: Q 89. (page 609)

Potato power problems Refer to Exercises 85 and 87

a. Explain one disadvantage of using 伪=0.10 instead of 伪=0.05 when

performing the test.

b. Explain one disadvantage of taking a random sample of 500 potatoes instead of 250 potatoes from the shipment.

Short Answer

Expert verified

Part (a) There is the most likely to have a type I error

Part (b) More time-consuming and costly to collect the data.

Step by step solution

01

Part (a) Step 1: Given information

H0:p=0.08Ha:p>0.08,p=0.11,n=500伪=0.05
02

Part (a) Step 2: Explanation

Type I error: Reject the null hypothesis H0, once the null hypothesis H0

is true.

伪Showing the probability of a type I error.

If you increase 伪=0.05to伪=0.10 the likelihood of making a type I error increases, and you're more likely to make one, which is a negative.

03

Part (b) Step 1: Explanation

If the sample size is increased from 250 to 500 potatoes, data collection will be more time-consuming and costly for the 500 potatoes than for the 250 potatoes (as there are twice as many potatoes about which we need to collect data).

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Most popular questions from this chapter

Do you Tweet? The Pew Internet and American Life Project asked a random sample of U.S. adults, 鈥淒o you ever 鈥� use Twitter or another service to share updates about yourself or to see updates about others?鈥� According to Pew, the resulting 95% confidence interval is (0.123, 0.177).11 Based on the confidence interval, is there convincing evidence that the true proportion of U.S. adults who would say they use Twitter or another service to share updates differs from 0.17? Explain your reasoning.

In a test ofH0:p=0.4against Ha:p鈮�0.4, a random sample of size 100 yields a standardized test statistic of z=1.28. Which of the following is closest to the P-value for this test?

a. 0.90

b. 0.40

c. 0.05

d. 0.20

e. 0.10

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.

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?

An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. A commentator believes that more than half of all adults favor such a ban. The null and alternative hypotheses you would use to test this claim are

邪.H0:p鈭�=0.5;Ha:p鈭�>0.5H0:p^=0.5;Ha:p^>0.5.

b. H0:p=0.5;Ha:p>0.5H0:p=0.5;Ha:p>0.5.

c. H0:p=0.5;Ha:p<0.5H0:p=0.5;Ha:p<0.5.

d. H0:p=0.5;Ha:p鈮�0.H0:p=0.5;Ha:p鈮�0.5.

e. H0:p>0.5;Ha:p=0.5H0:p>0.5;Ha:p=0.5.
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