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Chapter 9: Q 89. (page 609)

Potato power problems Refer to Exercises 85 and 87

a. Explain one disadvantage of using α=0.10 instead of α=0.05 when

performing the test.

b. Explain one disadvantage of taking a random sample of 500 potatoes instead of 250 potatoes from the shipment.

Short Answer

Expert verified

Part (a) There is the most likely to have a type I error

Part (b) More time-consuming and costly to collect the data.

Step by step solution

01

Part (a) Step 1: Given information

H0:p=0.08Ha:p>0.08,p=0.11,n=500α=0.05
02

Part (a) Step 2: Explanation

Type I error: Reject the null hypothesis H0, once the null hypothesis H0

is true.

αShowing the probability of a type I error.

If you increase α=0.05toα=0.10 the likelihood of making a type I error increases, and you're more likely to make one, which is a negative.

03

Part (b) Step 1: Explanation

If the sample size is increased from 250 to 500 potatoes, data collection will be more time-consuming and costly for the 500 potatoes than for the 250 potatoes (as there are twice as many potatoes about which we need to collect data).

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Most popular questions from this chapter

Side effects A drug manufacturer claims that less than 10%of patients who take its new drug for treating Alzheimer’s disease will experience nausea. To test this claim, researchers conduct an experiment. They give the new drug to a random sample of 300out of 5000Alzheimer’s patients whose families have given informed consent for the patients to participate in the study. In all, 25of the subjects experience nausea.

a. Describe a Type I error and a Type II error in this setting, and give a possible

consequence of each.

b. Do these data provide convincing evidence for the drug manufacturer’s claim?

Don’t argue Refer to Exercises 2 and 12.

a. What conclusion would you make at the α=0.01 level?

b. Would your conclusion from part (a) change if a 5% significance level was used

instead? Explain your reasoning.

Don't argue! A Gallup poll report revealed that 72%of teens said they seldom or never argue with their friends. 3Yvonne wonders whether this result holds true in her large high school, so she surveys a random sample of 150students at her school.

state appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest

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.

Tests and confidence intervals The P-value for a two-sided test of the null hypothesis H0:μ=10is0.06

a. Does the 95% confidence interval for μ include 10? Why or why not?

b. Does the 90% confidence interval for μ include 10? Why or why not?
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