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Chapter 9: Q 108. (page 611)

A researcher plans to conduct a significance test at the 伪=0.01 significance 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 II error for the particular alternative value of the parameter she used is

a.0.01.b.0.10.c.0.89.d.0.90.e.0.99.

Short Answer

Expert verified

The correct option is (b) 0.10

Step by step solution

01

Given information

伪=0.01

02

Explanation

The most appropriate response to the given statement "A researcher intends to conduct a significance test with a significance level of 伪=0.01. She plans for a power of 0.90for a certain alternative value of the parameter of interest in her investigation. She computed the power at a certain alternative value of the parameter, the risk of the researcher making a Type II error is 0.10"

Power is calculated in this case as,

1鈭�P(Type2error)P(Type2error)+Power=1P(Type2error)=1鈭�PowerP(Type2error)=1鈭�0.90P(Type2error)=0.10

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Most popular questions from this chapter

18%Members of the city council want to know if a majority of city residents supports a 1%increase in the sales tax to fund road repairs. To investigate, they survey a random sample of 300city residents and use the results to test the following hypotheses:

H0:p=0.50

Ha:p>0.50

where pis the proportion of all city residents who support a 1%increase in the sales tax to fund road repairs.

In the sample, p^=158/300=0.527, The resulting P-value is 0.18. What is the correct interpretation of this P-value?

a. Only 18% of the city residents support the tax increase.

b. There is an 18%chance that the majority of residents supports the tax increase.

c. Assuming that 50%of residents support the tax increase, there is an 18%probability that the sample proportion would be 0.527or greater by chance alone.

d. Assuming that more than 50%of residents support the tax increase, there is an 18%probability that the sample proportion would be 0.527or greater by chance alone.

e. Assuming that 50%of residents support the tax increase, there is an 18% chance that the null hypothesis is true by chance alone.

Clean water The Environmental Protection Agency (EPA) has determined that safe

drinking water should contain at most 1.3mg/liter of copper, on average. A water supply company is testing water from a new source and collects water in small bottles at each of30randomly selected locations. The company performs a test at the 伪=0.05 significance level ofH0:渭=1.3versus Ha:渭>1.3, where 渭 is the

true mean copper content of the water from the new source.

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 company鈥檚 choice of 伪=0.05? Why or why not?

Ski jump When ski jumpers take off, the distance they fly varies considerably depending on their speed, skill, and wind conditions. Event organizers must position the landing area to allow for differences in the distances that the athletes fly. For a particular competition, the organizers estimate that the variation in distance flown by the athletes will be \(\sigma=10\) \(\sigma=10\) meters. An experienced jumper thinks that the organizers are underestimating the variation.

Attitudes Refer to Exercises 4 and 10 . What conclusion would you make at the 伪=0.05 level?

Cell-phone passwords A consumer organization suspects that less than half of parents know their child鈥檚 cell-phone password. The Pew Research Center asked a random sample of parents if they knew their child鈥檚 cell-phone password. Of the 1060parents surveyed, 551reported that they knew the password. Explain why it isn鈥檛 necessary to carry out a significance test in this setting.
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