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Chapter 9: Q. 77 (page 589)

The power of tomatoes The researchers who carried out the experiment in Exercise 75suspect that the large P-value (0.114) is due to low power.

(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 .

Short Answer

Expert verified

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

b. Increasing the significance level, decreasing the standard deviation sxor increasing the sample size.

Step by step solution

01

Given information

The researchers who carried out the experiment in Exercise 75suspect that the large P-value (0.114) is due to low power.

02

Explanation (part a)

Type I error: experts conclude that Variety A has a higher mean yield when it actually doesn’t.

Type II error: experts conclude that there is no mean difference in yields when, in fact,

Variety A has a higher mean yield.

Type II error since we failed to reject H0.

03

Explanation (part b)

Increasing the significance level, decreasing the standard deviation sxor increasing the sample size.

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Most popular questions from this chapter

After checking that conditions are met, you perform a significance test of H0:μ=1versus Hα:μ≠1. You obtain a Pvalue of 0.022. Which of the following is true?

(a) A95%confidence interval for μwill include the value 1

(b) A 95%confidence interval forμwill include the value 0.

(c) A99% confidence interval forμwill include the value 1

(d) A 99%confidence interval for μwill include the value 0

(e) None of these is necessarily true.

Sampling shoppers A marketing consultant observes 50 consecutive shoppers at a supermarket, recording how much each shopper spends in the store. Explain why it would not be wise to use these data to carry out a significance test about the mean amount spent by all shoppers at this supermarket.

Tests and CIs The P-value for a one-sided test of the null hypothesisH0:μ=15is 0.03.

(a) Does the 99%confidence interval for μinclude 15? Why or why not?

(b) Does the 95%confidence interval for μinclude 15? Why or why not?

Explain in plain language why a significance test that is significant at the 1% level must always be significant at the 5% level. If a test is significant at the 5% level, what can you say about its significance at the 1% level?

You are testing H0:μ=10against Hα:μ≠10based on an SRS of 15tobservations from a Normal population. What values of the statistic are statistically significant at theα=0.005level?

(a) t>3.326

(b) t>3.286

(c) t>2.977

(d) t<-3.326ort>3.326

(c)t<-3.286ort>3.286
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