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Chapter 9: Q. 78 (page 589)

Study more! The significance test in Exercise 76yields a P-value of 0.0622.

(a) Describe a Type I and a Type II error in this setting. Which type of error could you have made in Exercise 76? Why?

(b) Which of the following changes would give the test a higher power to detect 渭=120minutes: using 伪=0.01or 伪=0.10? Explain.

Short Answer

Expert verified

a. Type II error since we failed to reject H0.

b. both 伪=0.01and伪=0.1give the higher power.

Step by step solution

01

Given information

The significance test in Exercise 76yields a P-value of 0.0622.

02

Explanation (part a)

Type I error: experts conclude that student study hours has a higher mean yield when it actually doesn鈥檛.

Type II error: experts conclude that there is a mean difference in yields when, in fact,

student study hours has a higher mean yield.

Type II error since we failed to reject H0.

03

Explanation (part b)

z(s) test statistics is:

z(s)=(x-渭鈧赌)/s/鈭�nz(s)=-30/8.22z(s)=-3.65

p-value for that z(s) p-value=0

Then for 伪=0.01or0.1;p-value<0.01or0.1

We are in the rejection region we need to reject H鈧赌. Therefore, both localid="1650893185130" 伪=0.01and伪=0.1give the higher power.

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Most popular questions from this chapter

The most important condition for sound conclusions from statistical inference is that

(a) the data come from a well-designed random sample or randomized experiment

(b) the population distribution be exactly Normal.

(c) the data contain no outliers.

(d) the sample size be no more than 10%of the population size.

(c) the sample size be at least 30.

A random sample of 100likely voters in a small city produced 59voters in favor of Candidate A. The observed value of the test statistic for testing the null hypothesis H0:p=0.5versus the alternative hypothesis Ha:p=0.5is

(a)z=0.59-0.50.59(0.41)100

(b). z=0.59-0.50.5(0.5)100

(c). z=0.5-0.590.59(0.41)100

(d). z=0.5-0.590.5(0.5)100

(e).t=0.59-0.50.5(0.5)100

In planning a study of the birth weights of babies whose mothers did not see a doctor

before delivery, a researcher states the hypotheses as

H0:x炉=1000gramsHa:x炉<1000grams

(a) State hypotheses for a significance test to determine whether first responders are arriving within 8 minutes of the call more often. Be sure to define the parameter of interest.

(b) Describe a Type I error and a Type II error in this setting and explain the consequences of each.

(c) Which is more serious in this setting: a Type I error or a Type II error? Justify your answer.

(d) If you sustain a life-threatening injury due to a vehicle accident, you want to receive medical treatment as quickly as possible. Which of the two significance tests鈥�H0:渭=6.7versusHa:渭<6.7 or the one from part (a) of this exercise鈥攚ould you be

more interested in? Justify your answer.

An SRS of 100 postal employees found that the average time these employees had worked at the postal service was 7years with standard deviation 2years. Do these data provide convincing evidence that the mean time of employment M for the population of postal employees has changed from the value of 7.5 that was true 20years ago? To determine this, we test the hypotheses H0:渭=7.5versus Ha:渭鈮�7.5using a one-sample ttest. What conclusion should we draw at the 5%significance level?

(a) There is convincing evidence that the mean time working with the postal service has changed.

(b) There is not convincing evidence that the mean time working with the postal service has changed.

(c) There is convincing evidence that the mean time working with the postal service is still 7.5 years.

(d) There is convincing evidence that the mean time working with the postal service is now 7years.

(e) We cannot draw a conclusion at the 5% significance level. The sample size is too small.
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