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Chapter 9: Q 108. (page 611)

A researcher plans to conduct a significance test at the α=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

α=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 α=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−P(Type2error)P(Type2error)+Power=1P(Type2error)=1−PowerP(Type2error)=1−0.90P(Type2error)=0.10

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Most popular questions from this chapter

Packaging DVDs (6.2,5.3) A manufacturer of digital video discs (DVDs) wants to be sure that the DVDs will fit inside the plastic cases used as packaging. Both the cases and the DVDs are circular. According to the supplier, the diameters of the plastic cases vary Normally with mean μ=5.3inches and standard deviation σ=0.01inch. The DVD manufacturer produces DVDs with mean diameterμ=5.26inches. Their diameters follow a Normal distribution with σ=0.02inch.

a. Let X = the diameter of a randomly selected case and Y = the diameter of a randomly selected DVD. Describe the shape, center, and variability of the distribution of the random variable X−Y. What is the importance of this random variable to the DVD manufacturer?

b. Calculate the probability that a randomly selected DVD will fit inside a randomly selected case.

c. The production process runs in batches of 100 DVDs. If each of these DVDs is paired with a randomly chosen plastic case, find the probability that all the DVDs fit in their cases.

A95%confidence interval for the proportion of viewers of a certain reality television

show who are over 30 years old is (0.26,0.35). Suppose the show's producers want to est the hypothesis \H0:p=0.25against Ha: Ha:p≠0.25. Which of the following is an appropriate conclusion for them to draw at the α=0.05

a. Fail to reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old equals 0.25

b. Fail to reject H0there is not convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from0.25.

c. Reject H0; there is not convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from 0.25

. d. Reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old is greater than 0.25.

e. Reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from0.25.

Reporting cheating What proportion of students are willing to report cheating by other students? A student project put this question to an SRS of 172 undergraduates at a large university: “You witness two students cheating on a quiz. Do you go to the professor?” The Minitab output shows the results of a significance test and a 95% confidence interval based on the survey data.13

a. Define the parameter of interest.

b. Check that the conditions for performing the significance test are met in this case.

c. Interpret the P-value.

d. Do these data give convincing evidence that the population proportion differs from 0.15? Justify your answer with appropriate evidence.

1 A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay \(100 for the upgrade. For the upgrade to be profitable, the company must sell it to more than 20% of their customers. You contact a random sample of 60 customers and find that 16 would be willing to pay \)100 for the upgrade.

a. Do the sample data give convincing evidence that more than 20% of the company’s customers are willing to purchase the upgrade? Carry out an appropriate test at the α=0.05significance level.

b. Which would be a more serious mistake in this setting—a Type I error or a Type II error? Justify your answer.

c. Suppose that 30% of the company’s customers would be willing to pay $100 for the upgrade. The power of the test to detect this fact is0.60. Interpret this value.

Potato chips A company that makes potato chips requires each shipment of

potatoes to meet certain quality standards. If the company finds convincing evidence that more than 8%of the potatoes in the shipment have “blemishes,” the truck will be sent back to the supplier to get another load of potatoes. Otherwise, the entire truckload will be used to make potato chips. To make the decision, a supervisor will inspect a random sample of potatoes from the shipment. He will then perform a test of H0:p=0.08versus Ha:p>0.08, where p is the true proportion of potatoes with blemishes in a given truckload. The power of the test to detect that p=0.11, based on a random sample of 500 potatoes and significance level α=0.05, is 0.764Interpret this value.
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