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Chapter 10: Q. AP3.5 (page 701)

Which of the following will increase the power of a significance test?

a. Increase the Type II error probability.

b. Decrease the sample size.

c. Reject the null hypothesis only if the P-value is less than the significance level.

d. Increase the significance level α.

e. Select a value for the alternative hypothesis closer to the value of the null hypothesis.

Short Answer

Expert verified

The correct option is (d) Increase the significance levelα

Step by step solution

01

Given Information

We have to determine the theory that increase the power of a significance test.

02

Simplification

Atest'spowercanbeincreasedintwoways:byincreasingthesamplesizeorbyraisingthesignificancelevel.
As a result, increasing the power of a significance test with the help of the sigma's significance level.

Hence, the correct option is (d) Increase the significance levelα

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Most popular questions from this chapter

A beef rancher randomly sampled 42 cattle from her large herd to obtain a 95%confidence interval for the mean weight (in pounds) of the cattle in the herd. The interval obtained was (1010,1321). If the rancher had used a 98%confidence interval instead, the interval would have been

a. wider with less precision than the original estimate.

b. wider with more precision than the original estimate.

c. wider with the same precision as the original estimate.

d. narrower with less precision than the original estimate.

e. narrower with more precision than the original estimate.

Are teenagers going deaf? In a study of 3000randomly selected teenagers in 1990,450showed some hearing loss. In a similar study of 1800 teenagers reported in 2010,351showed some hearing loss.

a. Do these data give convincing evidence that the proportion of all teens with hearing

loss has increased at the α=0.01 significance level?

b. Interpret the P-value from part (a) in the context of this study.

The power takeoff driveline on tractors used in agriculture is a potentially serious hazard to operators of farm equipment. The driveline is covered by a shield in new tractors, but for a variety of reasons, the shield is often missing on older tractors. Two types of shields are the bolt-on and the flip-up. It was believed that the boll-on shield was perceived as a nuisance by the operators and deliberately removed, but the flip-up shield is easily lifted for inspection and maintenance and may be left in place. In a study initiated by the US National Safety Council, random samples of older tractors with both types of shields were taken to see what proportion of shields were removed. Of 183tractors designed to have bolt-on shields, 35had been removed. Of the 156tractors with flip-up shields, 15were removed. We wish to perform a test of H0:pb=pfversus Ha:pb>pf, where pband pfare the proportions of all the tractors with bolt-on and flip-up shields removed, respectively. Which of the following is not a condition for performing the significance test ?

(a) Both populations are Normally distributed.

(b) The data come from two independent samples.

(c) Both samples were chosen at random.

(d) The counts of successes and failures are large enough to use Normal calculations.

(e) Both populations are at least 10times the corresponding sample sizes.

Men versus women The National Assessment of Educational Progress (NAEP)

Young Adult Literacy Assessment Survey interviewed separate random samples of840

men and 1077women aged 21to 25years.

The mean and standard deviation of scores on the NAEP’s test of quantitative skills were x1=272.40and s1=59.2for the men in the sample. For the women, the results were x ̄2=274.73and s2=57.5.

a. Construct and interpret a 90% confidence interval for the difference in mean score for

male and female young adults.

b. Based only on the interval from part (a), is there convincing evidence of a difference

in mean score for male and female young adults?

Researchers suspect that Variety A tomato plants have a different average yield than Variety B tomato plants. To find out, researchers randomly select10Variety A and10Variety B tomato plants. Then the researchers divide in half each of10small plots of land in different locations. For each plot, a coin toss determines which half of the plot gets a Variety A plant; a Variety B plant goes in the other half. After harvest, they compare the yield in pounds for the plants at each location. The10differences (Variety A − Variety B) in yield are recorded. A graph of the differences looks roughly symmetric and single-peaked with no outliers. The mean difference is x-A-B=0.343051526=0.200=20%x-A-B=0.34and the standard deviation of the differences is s A-B=0.833051526=0.200=20%=sA-B=0.83.Let μA-B=3051526=0.200=20%μA−B = the true mean difference (Variety A − Variety B) in yield for tomato plants of these two varieties.

A 95% confidence interval forμA-B3051526=0.200=20%μA-Bis given by

a. 0.34±1.96(0.83)3051526=0.200=20%0.34±1.96(0.83)

b.0.34±1.96(0.8310)3051526=0.200=20%0.34±1.96(0.8310)

c. 0.34±1.812(0.8310)3051526=0.200=20%0.34±1.812(0.8310)

d. 0.34±2.262(0.83)3051526=0.200=20%0.34±2.262(0.83)

e.0.34±2.262(0.8310)3051526=0.200=20%0.34±2.262(0.8310)
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