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Chapter 12: Q.29 (page 794)

Recycle and Review Exercises 29-31 refer to the following setting. Does the color in which words are printed affect your ability to read them? Do the words themselves affect your ability to name the color in which they are printed? Mr. Starnes designed a study to investigate these questions using the 16 students in his AP Statistics class as subjects. Each student performed the following two tasks in random order while a partner timed his or her performance: (1) Read 32words aloud as quickly as possible, and (2) say the color in which each of32 words is printed as quickly as possible. Try both tasks for yourself using the word list given.

Color words (4.2) Let's review the design of the study-

a. Explain why this was an experiment and not an observational study.

b. Did Mr. Stames use a completely randomized design a: randomiz茅d black design? Why do you think he choose this experimental design?

c. Explain the purpose of the ramdom assignment in the context of the study.

Here are the data from Mr. Stames's experiment. For each subject, the time to perform the Iwo tasks is given to the nearest second.

Short Answer

Expert verified

(a) The reason for this is that each individual receives two treatments.so this is an experiment.

(b) Mr Stames use a completely randomized block design

(c) Where there is no random assignment, experience could be a confounding variable.

Step by step solution

01

Part (a) Step 1: Given Information

Given table is

We have to explain why this was an experiment and not an observational study .

02

Part (a) Step 2: Explanation

Individuals are given treatments in an experiment so that their reactions may be tracked.

An observational research seeks to collect data without interfering with the view they're looking at.

Experiment

The reason for this is that each individual receives two treatments (read words and say colours).

03

Part (b) Step 1: Given Information

The given table is

We have to determine did Mr. Stames use a completely randomized design a: randomiz茅d black design and why do you think he choose this experimental design .

04

Part (b) Step 2: Explanation

The reason for the randomized block design is that each subject received two treatments and so each subject constructs a block.

The other option (a truly randomized design) would need each participant to receive only one treatment, resulting in a cost of2

05

Part (c) Step 1: Given Information

The given table is

We have to explain the purpose of the ramdom assignment in the context of the study.

06

Part (c) Step 2: Explanation

When the effects of two variables on a response variable cannot be separated from one another, two variables are assumed.

To eliminate any potential confounding variations in the groups before the experiment might affect the output data, random assignment is employed to make various groups of persons as comparable as possible.

In this situation, the order in which the two treatments are mentioned is chosen at random to ensure that prior experience has no bearing on the outcome. They are more familiar with the list after the first treatment and are therefore more likely to get a better time on the second treatment. As a result, in situations where there is no random assignment, experience may be a confounding variable.

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Most popular questions from this chapter

Multiple Choice Select the best answer for Exercises 23-28. Exercises 23-28 refer to the following setting. To see if students with longer feet tend to be taller, a random sample of 25students was selected from a large high school. For each student, x=footlength&y=heightwere recorded. We checked that the conditions for inference about the slope of the population regression line are met. Here is a portion of the computer output from a least-squares regression analysis using these data:

Which of the following would have resulted in a violation of the conditions for inference?

a. If the entire sample was selected from one classroom

b. If the sample size was 15instead of 25

c. If the scatterplot of x=footlength&y=heightdid not show a perfect linear relationship

d. If the histogram of heights had an outlier

e. If the standard deviation of foot length was different from the standard deviation of height

Prey attracts predators Here is one way in which nature regulates the size of animal populations: high population density attracts predators, which remove a higher proportion of the population than when the density of the prey is low. One study looked at kelp perch and their common predator, the kelp bass. On each of four occasions, the researcher set up four large circular pens on sandy ocean bottoms off the coast of southern California. He randomly assigned young perch to 1of 4pens so that one pen had 10perch, one pen had 20perch, one pen had 40perch, and the final pen had 60perch. Then he dropped the nets protecting the pens, allowing bass to swarm in, and counted the number of perch killed after two hours. A regression analysis was performed on the 16data points using x=number of perch in pen and y=proportion of perch killed. Here is a residual plot and a histogram of the residuals. Check whether the conditions for performing inference about the regression model are met.

The following back-to-back stem plots compare the ages of players from two minor-league hockey teams (1/7=17 years)

Which of the following cannot be justified from the plots?

a. Team A has the same number of players in their 30sas does Team B.

b. The median age of both teams is the same.

c. Both age distributions are skewed to the right.

d. The range of age is greater for Team A

e. There are no outliers by the1.5IQR rule in either distribution.

A Harris poll found that 54%of American adults don鈥檛 think that human beings developed from earlier species. The poll鈥檚 margin of error for 95%confidence was 3%. This means that

a. there is a 95%chance the interval (51%,57%) contains the true per cent of American adults who do not think that human beings developed from earlier species.

b. the poll used a method that provides an estimate within 3% of the truth about the population in 95%of samples.

c. if Harris conducts another poll using the same method, the results of the second poll will lie between 51%and 57%

d. there is a 3% chance that the interval is incorrect.

e. the poll used a method that would result in an interval that contains 54%in95% of all possible samples of the same size from this population.

Exercises T12.4鈥揟12.8 refer to the following setting. An old saying in golf is 鈥淵ou drive for show and you putt for dough.鈥� The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of 69 of the nearly 1000 players on the PGA Tour鈥檚 world money list are examined. The average number of putts per hole (fewer is better) and the player鈥檚 total winnings for the previous season are recorded and a least-squares regression line was fitted to the data. Assume the conditions for
inference about the slope are met. Here is computer output from the regression analysis:

T12.8 Which of the following would make the calculation in Exercise T12.7 invalid?

a. If the scatterplot of the sample data wasn鈥檛 perfectly linear.

b. If the distribution of earnings has an outlier.

c. If the distribution of earnings wasn鈥檛 approximately Normal.

d. If the earnings for golfers with small putting averages was much more variable than the earnings for golfers with large putting averages.

e. If the standard deviation of earnings is much larger than the standard deviation of putting average.
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