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Chapter 4: Q 49. (page 253)

Effects of class size Do smaller classes in elementary school really benefit students in areas such as scores on standardized tests, staying in school, and going on to college? We might do an observational study that compares students who happened to be in smaller and larger classes in their early school years. Identify a lurking variable that may lead to confounding with

the effects of small classes. Explain how confounding might occur.

Short Answer

Expert verified

For example, the type of school (public/private).

Step by step solution

01

Given information

We must find a variable that may cause confounding with small-class effects and determine how confounding occurs.

02

Concept

A lurking variable is one that is not included in the study's explanatory or response variables but has the potential to influence the response variable.

03

Explanation

One potential hidden factor is the private vs. public school debate. Students at private schools may have classes and receive higher grades. There should be more about private schools: they contribute to performance rather than just having tiny class sizes.

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Most popular questions from this chapter

Sampling frame Ideally, the sampling frame in a sample survey should list every individual in the population, but in practice, this is often difficult.

Suppose that a sample of households in a community is selected at random from the telephone directory. Explain how this sampling method results in under coverage that could lead to bias.

Chocolate gets my heart pumping Cardiologists at Athens Medical School in Greece wanted to test whether chocolate affected blood flow in the blood vessels. The researchers recruited 17healthy young volunteers, who were each given a 3.5-ounce bar of dark chocolate, either bittersweet or fake chocolate.

On another day, the volunteers were switched. The subjects had no chocolate outside the study, and investigators didn’t know whether a subject had eaten the real or the fake chocolate. An ultrasound was taken of each volunteer’s upper arm to see the functioning of the cells in the walls of the main artery. The investigators found that blood vessel function was improved when the subjects ate bittersweet chocolate, and that there were no such changes when they ate the placebo (fake chocolate).

(a) What type of design did the investigators use in their study?

(b) Explain why the investigators chose this design instead of a completely randomized design.

(c) Why is it important to randomly assign the order of the treatments for the subjects?

Systematic random sample Sample surveys often use a systematic random sample to choose a sample of apartments in a large building or housing units in a block at the last stage of a multistage sample. Here is a description of how to choose a systematic random sample. Suppose that we must choose 4 addresses out of 100 Because 100/4=25 we can think of the list as four lists of 25 addresses. Choose 1 of the first 25 addresses at random using Table D. The sample contains this address and the addresses 25,50, and 75 places down the list from it. If the table gives 13, for example, then the systematic random sample consists of the addresses numbered 13,38,63, and 88

(a) Use Table D to choose a systematic random sample of 5 addresses from a list of 200 Enter the table at line 120

(b) Like an SRS, a systematic random sample gives all individuals the same chance to be chosen. Explain why this is true. Then explain carefully why a systematic sample is not an SRS.

In the cornfield An agriculture researcher wants to compare the yield of five corn varieties: A, B, C, D, and E. The field in which the experiment will be carried out increases in fertility from north to south. The researcher therefore divides the field into twenty five plots of equal size, arranged in five east–west rows of five plots each, as shown in the diagram.

(a) Explain why a randomized block design would be better than a completely randomized design in this setting.

(b) Should the researcher use the rows or the columns of the field as blocks? Justify your answer.

(c) Use technology or Table D to carry out the random assignment required by your design. Explain your method clearly.

An example of a non-sampling error that can reduce the accuracy of a sample survey is

(a) using voluntary response to choose the sample.

(b) using the telephone directory as the sampling frame.

(c) interviewing people at shopping malls to obtain a sample.

(d) variation due to chance in choosing a sample at random.

(e) inability to contact many members of the sample.
See all solutions

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