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Chapter 9: Q.77 (page 589)

(a) Describe a Type I and a Type II error in this setting. Which type of error could you have made in Exercise 75? Why?

(b) Explain two ways that the researchers could have increased the power of the test to detect 渭=0.5.

Short Answer

Expert verified

a. A type II error has been made

b. increasing the significance level and increasing the sample size

Step by step solution

01

Introduction

The significance level of an occasion (like a statistical test) is the probability that the occasion might have happened by some coincidence. If the level is quite low, that is to say, the probability of occurring by chance is minuscule, we say the occasion is significant.

02

Explanation Part (a)

Type-I error is when Variety A has a higher mean yield than Variety B which is incorrect as it is really not.

Type-II error is when Variety A has a lower mean yield than Variety B which is incorrect as really Variety A has a higher yield.

A type II error has been made as it is known that variety A has a higher yield.

03

Explanation Part (b)

The two ways that the researchers could have increased the power of the test are-

Increasing the significance level and increasing the sample size.

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Most popular questions from this chapter

Roulette an American roulette wheel has 18red slots among its 38slots.In a random sample of 50pins,the ball lands in a red slot 31times.

(a) Do the data give convincing evidence that the wheel is unfair? Carry out an appropriate test at the伪=0.05significance level to help answer this question.

(b) The casino manager uses your data to produce a 99%confidence interval for pand gets role="math" localid="1650358305073" 0.44,0.80. He says that this interval provides convincing evidence that the wheel is fair. How do you respond?

- If conditions are met, conduct a one-sample \(t\) test about a population mean \(\mu\).

Eye black Athletes performing in bright sunlight often smear black grease under their eyes to reduce glare. Does cye black work? In one experiment, 16 randomly selected student subjects took a test of sensitivity to contrast after 3 hours facing into bright sun, both with and without eye black. Here are the differences in sensitivity, with eye black mines without eye black:

0.070.64-0.12-0.05-0.180.14-0.160.03
0.050.020.430.24-0.110.280.050.29

We want to know whether cye black increases sensitivity an the average.

(a) State hypotheses, Be sure to define the parameter.

(b) Check conditions for carrying out a significance test.

(c) ThePvalueof the test is 0.047. Interpet this value in context.

- Interpret a Type l error and a Type ll error in context, and give the consequences of each.

- Understand the relationsonship between the significance level at a test P(Type li error), and power.

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.

Is it significant? For students without special preparation, SAT Math scores in recent years have varied Normally with mean 渭=518. One hundred students go through a rigorous training program designed to raise their SAT Math scores by improving their mathematics skills. Use your calculator to carry out a test of

H0:渭=518

H伪:渭>518

in each of the following situations.

(a) The students' scores have mean x炉=536.7and standard deviation sx=114. Is this result significant at the5%level?

(b) 'The students' scores have mean x=537.0and standard deviation sx=114. Is this result significant at the 5%level?

(c) When looked at together, what is the intended lesson of (a) and (b)?

In a test of H0:p=0.4against Ha:p鈮�0.4, a random sample of size 100yields a test statistic of z=1.28. The P-value of the test is approximately equal to

(a) 0.90.

(b) 0.40.

(c) 0.05.

(d) 0.20.

(e) 0.10.
See all solutions

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