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Chapter 10: Q.9 (page 622)

Explain why the conditions for using two-sample z procedures to perform inference about p1-p2are not met in the settings

Shrubs and fire Fires are a serious threat to shrubs in dry climates. Some shrubs can resprout from their roots after their tops are destroyed. One study of resprouting took place in a dry area of Mexico.7The investigators randomly assigned shrubs to treatment and control groups. They clipped the tops of all the shrubs. They then applied a propane torch to the stumps of the treatment group to simulate a fire. All 12of the shrubs in the treatment group were resprouted. Only 8 of the 12 shrubs in the control group were resprouted.

Short Answer

Expert verified

From the given information, here, success in the treatment group is 8which is less than 10. It implies that the normality assumption is not fulfilled here.

So, the two-proportion z -test is not appropriate in this case.

Step by step solution

01

Given Information

It is given in the question that, for treatment group

Number of success (x)=8

Number of events(n)=12

02

Step 2: Explanation

To conduct the two-proportion z -test, the number of successes in both samples must be more than 10. Here, success in the treatment group is 8which is less than 10. It implies that the normality assumption is not fulfilled here.

So, the two-proportion z -test is not appropriate in this case.

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Most popular questions from this chapter

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 bolt-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 U.S. 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, 35 had been removed. Of the 136 tractors with flip-up shields, 15 were removed. We wish to perform a test of H0:pb-pif versus Ha:pb≠pf where pb and pf are the proportions of all tractors with the bolt-on and flip-up shields removed, respectively. Which of the following conditions for performing the appropriate significance test is definitely not satisfied in this case?

(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 10 times the corresponding sample sizes

A random sample of 100 of a certain popular car model last year found that 20 had a certain minor defect in the brakes. The car company made an adjustment in the production process to try to reduce the proportion of cars with the brake problem. A random sample of 350 of this year's model found that 50 had the minor brake defect.

(a) Was the company's adjustment successful? Carry out an appropriate test to support your answer.

(b) Describe a Type I error and a Type Il error in this setting, and give al possible consequence of each.

Quality control (2.2,5.3,6.3)Many manufacturing companies use statistical techniques to ensure that the products they make meet standards. One common way to do this is to take a random sample of products at regular intervals throughout the production shift. Assuming that the process is working properly, the mean measurements from these random samples will vary Normally around the target mean μ, with a standard deviation of σ. For each question that follows, assume that the process is working properly.

(a) What's the probability that at least one of the next two sample means will fall more than 2σfrom the target mean μ? Show your work.

(b) What's the probability that the first sample mean that is greater than μ+2σis the one from the fourth sample taken?

(c) Plant managers are trying to develop a criterion for determining when the process is not working properly. One idea they have is to look at the 5 most recent sample means. If at least 4of the 5 fall outside the interval(μ-σ,μ+σ), they will conclude that the process isn't working. Is this a reasonable criterion? Justify your answer with an appropriate probability.

Preventing drowning Drowning in bathtubs is a major cause of death in children less than 5 years old. A random sample of parents was asked many questions related to bathtub safety. Overall, 85% of the sample said they used baby bathtubs for infants. Estimate the percent of all parents of young children who use baby bathtubs.

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

(a) Increase the Typeιιerror probability.

(b) Increase the sample size.

(c) Reject the null hypothesis only if the P-value is smaller than the level of significance.

(d) Decrease the significance level α.

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