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Statistics For Business And Economics

James T. McClave, P. George Benson, Terry Sincich

$Math Studyset Vaia Explanations$ Math

13th Edition · 888 pages

ISBN: 9780134506593

Chapter 8: Q2E (page 458)

What are the treatments for a designed experiment with two factors, one qualitative with two levels (A and B) and one quantitative with five levels (50, 60, 70, 80, and 90)?

Short Answer

Expert verified

There are ten treatments (A,50), (A,60), (A,70), (A,80), (A,90), (B,50), (B,60), (B,70), (B,80), (B,90).

Step by step solution

01

Given Information

There are two factors, one with levels (A and B) and the other with five levels 50, 60, 70, 80, and 90.

02

Definition

The treatments for two factors are the different combinations of the levels of two factors.

03

Identifying the treatments

Two factors are qualitative with two levels and quantitative with five levels.

Therefore the treatments are a combination of these two factors levels. The treatments are (A,50), (A,60), (A,70), (A,80), (A,90), (B,50), (B,60), (B,70), (B,80), (B,90).

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Most popular questions from this chapter

Fingerprint expertise.A study published in PsychologicalScience(August 2011) tested the accuracy of experts andnovices in identifying fingerprints. Participants were presentedpairs of fingerprints and asked to judge whetherthe prints in each pair matched. The pairs were presentedunder three different conditions: prints from the same individual (match condition), non-matching but similar prints (similar distracter condition), and nonmatching and very dissimilar prints (non-similar distracter condition). The percentages of correct decisions made by the two groups under each of the three conditions are listed in the table.

Conditions	Fingerprints expert	Novices
Match similar	92.12%	74.55%
Distracter	99.32%	44.82%
Non-similar distracter	100%	77.03%

a.Given a pair of matched prints, what is the probability that an expert failed to identify the match?

b. Given a pair of matched prints, what is the probabilitythat a novice failed to identify the match?

c. Assume the study included 10 participants, 5 experts and 5 novices. Suppose that a pair of matched prints was presented to a randomly selected study participant and the participant failed to identify the match. Is the participant more likely to be an expert or a novice?

Consider the discrete probability distribution shown here.

x	10	12	18	20
p	.2	.3	.1	.4

a. Calculate $μ, σ^{2}$ and $σ$ .

b. What is $P (x < 15)$ ?

c. Calculate $μ \pm 2 σ$ .

d. What is the probability that xis in the interval $μ \pm 2 σ$ ?

Given that x is a random variable for which a Poisson probability distribution provides a good approximation, use statistical software to find the following:

a. $P (x ⩽ 2)$ when $λ = 1$

b. $P (x ⩽ 2)$ when $λ = 2$

c. $P (x ⩽ 2)$ when $λ = 3$

d. What happens to the probability of the event ${x ⩽ 2}$ as $λ$ it increases from 1 to 3? Is this intuitively reasonable?

Question: Performance ratings of government agencies. The U.S. Office of Management and Budget (OMB) requires government agencies to produce annual performance and accounting reports (PARS) each year. A research team at George Mason University evaluated the quality of the PARS for 24 government agencies (The Public Manager, Summer 2008), where evaluation scores ranged from 12 (lowest) to 60 (highest). The accompanying file contains evaluation scores for all 24 agencies for two consecutive years. (See Exercise 2.131, p. 132.) Data for a random sample of five of these agencies are shown in the accompanying table. Suppose you want to conduct a paired difference test to determine whether the true mean evaluation score of government agencies in year 2 exceeds the true mean evaluation score in year 1.

Source: J. Ellig and H. Wray, “Measuring Performance Reporting Quality,” The Public Manager, Vol. 37, No. 2, Summer 2008 (p. 66). Copyright © 2008 by Jerry Ellig. Used by permission of Jerry Ellig.

a. Explain why the data should be analyzedusing a paired difference test.

b. Compute the difference between the year 2 score and the year 1 score for each sampled agency.

c. Find the mean and standard deviation of the differences, part

b. Use the summary statistics, part c, to find the test statistic.

e. Give the rejection region for the test using a = .10.

f. Make the appropriate conclusion in the words of the problem.

Question: Two independent random samples have been selected—100 observations from population 1 and 100 from population 2. Sample means ${\bar{x}}_{1} =26.6, {\bar{x}}_{2} = 15.5$ were obtained. From previous experience with these populations, it is known that the variances are ${σ_{1}}^{2} = 9 a n d {σ_{2}}^{2} = 16$ .

a. Find $σ_{({\bar{x}}_{1} - {\bar{x}}_{2})}$ .

b. Sketch the approximate sampling distribution for $({\bar{x}}_{1} - {\bar{x}}_{2})$ , assuming $(μ_{1} - μ_{2}) = 10$ .

c. Locate the observed value of $({\bar{x}}_{1} - {\bar{x}}_{2})$ the graph you drew in part

b. Does it appear that this value contradicts the null hypothesis $H_{0} : (μ_{1} - μ_{2}) = 10$ ?

d. Use the z-table to determine the rejection region for the test against $H_{0} : (μ_{1} - μ_{2}) \neq 10$ . Use $α = 0.5$ .

e. Conduct the hypothesis test of part d and interpret your result.

f. Construct a confidence interval for $(μ_{1} - μ_{2})$ . Interpret the interval.

g. Which inference provides more information about the value of $(μ_{1} - μ_{2})$ — the test of hypothesis in part e or the confidence interval in part f?

See all solutions

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