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Chapter 9: Q.30 (page 548)

A researcher plans to conduct a significance test at the 伪=0.01significance level. She designs her study to have a power of 0.90 at a particular alternative value of the parameter of interest. The probability that the researcher will commit a Type Il error for the particular alternative value of the parameter at which she computed the power is

(a) 0.01

(b) 0.10

(c) 0.89

(d) 0.90

(c) 0.99

Short Answer

Expert verified

The probability that the researcher will commit a Type Il error for the particular alternative value of the parameter at which she computed the power is option b.0.10

Step by step solution

01

Introduction

A type I error is a sort of issue that happens during the speculation testing process when an invalid theory is dismissed, despite the fact that it is precise and ought not to be dismissed.

02

Explanation

Given,

A researcher plans to conduct a significance test at the 伪=0.01significance level.

power = 0.90

Probabilty of type II error = 1-power

=1-0.90=0.10

Hence option b. 0.10is correct

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Most popular questions from this chapter

(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.

Which of the following 95% confidence intervals would lead us to reject H0:p=0.30in favor of Ha:p鈮�0.30at the 5% significance level?

(a) (0.29, 0.38) (c) (0.27, 0.31) (e) None of these

(b) (0.19, 0.27) (d) (0.24, 0.30)

The z statistic for a test of H0 :p = 0.4 versus Ha : p > 0.4 is z = 2.43. This test is

(a) not significant at either 伪=0.05or 伪=0.01.

(b) significant at 伪=0.05but not at 伪=0.01

(c) significant at 伪=0.01but not at 伪=0.05.

(d) significant at both 伪=0.05and 伪=0.01.

(e) inconclusive because we don鈥檛 know the value of 藛p .

Significance and sample size A study with 5000 subjects reported a result that was statistically significant at the 5% level. Explain why this result might not be particularly large or important.

Bottles of a popular cola are supposed to contain 300milliliters (ml) of cola. There is some variation from bottle to bottle because the filling machinery is not perfectly precise. From experience, the distribution of the contents is approximately Normal. An inspector measures the contents of six randomly selected bottles from a single day鈥檚 production. The results are 299.4297.7301.0298.9300.2297.0Do these data provide convincing evidence that the mean amount of cola in all the bottles filled that day differs from the target value of 300ml? Carry out an appropriate test to support your answer
See all solutions

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