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Chapter 12: Q. AP4.1 (page 827)

Section I: Multiple ChoiceChoose the best answer for Questions AP4.1鈥揂P4.40.
AP4.1 A major agricultural company is testing a new variety of wheat to determine whether it is more resistant to certain insects than the current wheat variety. The proportion of a current wheat crop lost to insects is 0.04. Thus, the company wishes to test the following hypotheses:
H0:p=0.04

Ha:p<0.04

Which of the following significance levels and sample sizes would lead to the highest power for this test?
a. n=200 and 伪=0.01
b. n=400and 伪=0.05
c.n=400and 伪=0.01
d. n=500and 伪=0.01
e. n=500 and 伪=0.05

Short Answer

Expert verified

The correct answer is option (e) n=500 and 伪=0.05.

Step by step solution

01

Given information

To determine the significance levels and sample sizes that lead to the highest power for the test.

02

Explanation

A large agricultural corporation is evaluating a new wheat type to see if it is more bug resistant than the current wheat variety. While the power for a given value of the alternative can potentially be calculated.

Simple notions can be used to address the question:
The larger the sample size size, better possible it is to identify variations.
The lower the power, the more difficult it is to reject the null hypothesis, and the more likely you are to commit a type Il error.
As a result, when alpha and sample size are both large, the power is maximized.
As a result, option (e) is the proper answer.

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Most popular questions from this chapter

T12.9 Which of the following would provide evidence that a power model of the form y=axp, wherep鈮�0and p鈮�1, describes the relationship between a response variable y and an explanatory variable x?
a. A scatterplot of y versus x looks approximately linear.
b. A scatterplot of Iny versus x looks approximately linear.
c. A scatterplot of y versus lnx looks approximately linear.
d. A scatterplot of Iny versus lnx looks approximately linear.
e. None of these

T12.10We record data on the population of a particular country from 1960 to 2010. A
scatterplot reveals a clear curved relationship between population and year. However, a different scatterplot reveals a strong linear relationship between the logarithm (base 10) of the population and the year. The least-squares regression line for the transformed data is
log(population)=^鈭�13.5+0.01(year)
Based on this equation, which of the following is the best estimate for the population of the country in the year 2020?
a. 6.7
b. 812
c. 5,000,000
d. 6,700,000
e. 8,120,000

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.

A scatterplot of yversus xshows a positive, nonlinear association. Two different transformations are attempted to try to linearize the association: using the logarithm of the y-values and using the square root of the y-values. Two least-squares regression lines are calculated, one that uses x to predict log(y) and the other that uses x to predict y. Which of the following would be the best reason to prefer the least-squares regression line that uses x to predict log(y)?

a. The value of r2is smaller.

b. The standard deviation of the residuals is smaller.

c. The slope is greater.

d. The residual plot has more random scatter.

e. The distribution of residuals is more Normal.

Random assignment is part of a well-designed comparative experiment because

a. it is fairer to the subjects.

b. it helps create roughly equivalent groups before treatments are imposed on the subjects.

c. it allows researchers to generalize the results of their experiment to a larger population.

d. it helps eliminate any possibility of bias in the experiment.

e. it prevents the placebo effect from occurring.
See all solutions

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