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Chapter 9: Q 93. (page 609)

Error probabilities and power You read that a significance test at the 伪=0.01

significance level has probability 0.14of making a Type II error when a specific alternative is true.

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

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

Short Answer

Expert verified

Part (a) Power =0.86=86%

Part (b) P (Type I error) =0.01=1%

Step by step solution

01

Part (a) Step 1: Given information

P (Type II error) =0.14

伪=0.01

02

Part (a) Step 2: Calculation

The power is the complement of the probability of type II error, therefore the power isPower=1-P(TypeIIerror)=1鈭�0.14=0.86=86%

03

Part (b) Step 1: Explanation

The significance level 伪shows the probability of type I error.

P(TypeIerror)=伪=0.01=1%

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Most popular questions from this chapter

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

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

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

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.

A Type I error in the context of this study occurs if the city council

a. finds convincing evidence that a majority of residents supports the tax increase, when in reality there isn鈥檛 convincing evidence that a majority supports the increase.

b. finds convincing evidence that a majority of residents supports the tax increase, when in reality at most 50%of city residents support the increase.

c. finds convincing evidence that a majority of residents supports the tax increase, when in reality more than 50%of city residents do support the increase.

d. does not find convincing evidence that a majority of residents supports the tax increase, when in reality more than 50%of city residents do support the increase.

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.

Teen drivers A state鈥檚 Division of Motor Vehicles (DMV) claims that 60%

of all teens pass their driving test on the first attempt. An investigative reporter examines an SRS of the DMV records for 125teens; 86of them passed the test on their first try. Is there convincing evidence at the 伪=0.05significance level that the DMV鈥檚 claim is incorrect?

How much juice? One company鈥檚 bottles of grapefruit juice are filled by a machine that is set to dispense an average of 180 milliliters (ml) of liquid. The company has been getting negative feedback from customers about underfilled bottles. To investigate, a quality-control inspector takes a random sample of 40 bottles and measures the volume of liquid in each bottle. The mean amount of liquid in the bottles is 179.6 ml and the standard deviation is 1.3 ml. Do these data provide convincing evidence at the伪=0.05significance level that the machine is underfilling the bottles?
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