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Chapter 13: Q. 14 (page 547)

Losses to Robbery. The Federal Bureau of investigation conducts surveys to obtain information on the value of losses from various types of robberies. Results of the surveys are published in Population-at-Risk Rates and Selected Crime indicators, Independent simple random samples of reports for three types of robberies-highway, gas station, and convenience store gave the following data, in dollars, on the value of losses.

a. What does MSTR measure?

b. What does MSE measure?

c. Suppose that you want to perform a one-way ANOVA to compare the mean losses among the three types of robberies. What conditions are necessary? How crucial are those conditions?

Short Answer

Expert verified

(a) The MSTR compares the sample means of the three different types of robberies.

(b) MSE quantifies the variation among the three robberies' sample means.

(c) The first and last conditions are extremely tough to break because there is no other way to do it. If the distribution is approximately normal, the second condition, we can use one-way ANOVA. If the sample sizes are about comparable, the third criterion can be broken.

Step by step solution

01

Part (a) Step 1: Given information

The given data is

02

Part (a) Step 2: Explanation

The MSTR mean sum of squares therapy.

Losses from three different sorts of robberies.

As a result, the sum of squares mean treatment assesses the changes in the sample means.

As a result, the MSTR compares the sample means of the three different types of robberies.

03

Part (b) Step 1: Given information

The given data is

04

Part (b) Step 2: Explanation

The MSE stands for mean squared error. It calculates the changes in data samples.

As a result, MSE quantifies the variation among the three robberies' sample means.

05

Part (c) Step 1: Given information

The given data is

06

Part (c) Step 2: Explanation

The necessary conditions are

- Simple random samples,

- normal populations,

- equal standard deviations,

- independent random samples.

The first and last conditions are extremely tough to break because there is no other way to do it. If the distribution is approximately normal, the second condition, we can use one-way ANOVA. If the sample sizes are about comparable, the third criterion can be broken.

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Most popular questions from this chapter

Income by Age. The U.S. Census Bureau collects information on the incomes of employed persons and publishes the results in Historical Income Tables. Independent simple random samples of 100cm- ployed persons in each of four age groups gave the data on annual income, in thousands of dollars, presented on the WeissStats site.

a. Obtain individual normal probability plots and the standard deviations of the samples.

b. Perform a residual analysis.

c. Decide whether presuming that the assumptions of normal populations and equal standard deviations are met is reasonable.
SAMPLE 1SAMPLE 2SAMPLE 3
1104
9416

810

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Suppose that a one-way ANOVA is being performed to compare the means of three populations and that the sample sizes are 10,12and 15. Determine the degrees of freedom for the F-statistic.

Artificial Teeth: Hardness. In a study by J. Zeng et al., three materials for making artificial teeth-Endura, Duradent, and Dura cross_were tested for hardness. Their results were published as the paper "In Vitro Wear Resistance of Three Types of Composite Resin Denture Teeth" (Journal of Prosthetic Dentistry, Vol. 94 , Issue 5, pp. 453-457). The Vickers microhardness (VHN) of the occlusal surfaces was measured with a load of 50 grams and a loading time of 30 seconds. Six pairs of teeth were tested for each material. The data on the Weiss Stats site are based on the results obtained by the researchers. At the 5\% significance level, do the data provide sufficient evidence to conclude that there is a difference in mean hardness among the three materials?
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