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Chapter 9: Q 94. (page 609)

Power and error A scientist calculates that a test at the α=0.05 significance level has probability 0.23 of making a Type II error when a specific alternative is true.

a. What is the power of the test against this alternative?

b. What’s the probability of making a Type I error?

Short Answer

Expert verified

Part (a) Power =0.77=77%

Part (b) P (Type I error) =0.05=5%

Step by step solution

01

Part (a) Step 1: Given information

P(TypeIIerror)=0.23

α=0.05

02

Part (a) Step 2: Calculation

The probability of a type II error is multiplied by the power.

Consequently, the power is

Power=1-P(TypeIIerror)=1−0.23=0.77=77%

03

Part (b) Step 1: Explanation

The type I error likelihood is represented by the significance level.

P(TypeIerror)=α=0.05=5%

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Most popular questions from this chapter

Which of the following 95%confidence intervals would lead us to reject H0:p=0.30in favor of Ha:pnotequalto0.30at the 5%significance level?

a. (0.19,0.27)

b.(0.24,0.30)

c. (0.27,0.31)

d. (0.29,0.31)

e. None of these

Powerful potatoes Refer to Exercise 85. Determine if each of the following

changes would increase or decrease the power of the test. Explain your answers.

a. Change the significance level to α=0.10

b. Take a random sample of 250 potatoes instead of 500 potatoes.

c. The true proportion is p=0.10 instead of p=0.11

Tests and confidence intervals The P-value for a two-sided test of the null hypothesis H0:μ=15is0.03

a. Does the 99% confidence interval for μ include 15? Why or why not?

b. Does the 95% confidence interval for μ include 15? Why or why not?

You are thinking of conducting a one-sample ttest about a population mean μusing a 0.05significance level. Which of the following statements is correct?

a. You should not carry out the test if the sample does not have a Normal distribution.

b. You can safely carry out the test if there are no outliers, regardless of the sample size.

c. You can carry out the test if a graph of the data shows no strong skewness, regardless of the sample size.

d. You can carry out the test only if the population standard deviation is known.

e. You can safely carry out the test if your sample size is at least 30 .

You are testing H0:μ=10 against Ha:μ≠10 based on an SRS of 15

observations from a Normal population. What values of the t statistic are statistically significant at the α=0.005 level?

a.t>3.326b.t>3.286c.t>2.977d.t<−3.326ort>3.326e.t<−3.286ort>3.286
See all solutions

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