A criminologist studying the relationship between level of education and crime rate in a counties collected the following data for a random sample of 84 counties: X is the percentage of individuals in the county having at least a high school diploma, and Y is the crime rate (crimes reported per 100,000 residents) last year. Assume that first order regression model Y₁ = ẞo + B₁X; + &; i = 1, 2, ..., 84 is appropriate. a. Test whether or not there is a linear association between crime rate and percentage of high school graduates, using a t test with a = 0.01. State the alternatives, decision rule, and conclusion. What is the P-value of the test? b. Suppose that the test in part (a) is to be carried out by means of a general linear test. State the full and reduced models. c. Obtain (1) SSE(F), (2) SSE(R), (3) dff, (4) dfR, (5) test statistic F* for the general linear test, (6) decision rule. d. Are the test statistic F* and the decision rule for the general linear test numerically equivalent to those in part (a)?
A criminologist studying the relationship between level of education and crime rate in a counties collected the following data for a random sample of 84 counties: X is the percentage of individuals in the county having at least a high school diploma, and Y is the crime rate (crimes reported per 100,000 residents) last year. Assume that first order regression model Y₁ = ẞo + B₁X; + &; i = 1, 2, ..., 84 is appropriate. a. Test whether or not there is a linear association between crime rate and percentage of high school graduates, using a t test with a = 0.01. State the alternatives, decision rule, and conclusion. What is the P-value of the test? b. Suppose that the test in part (a) is to be carried out by means of a general linear test. State the full and reduced models. c. Obtain (1) SSE(F), (2) SSE(R), (3) dff, (4) dfR, (5) test statistic F* for the general linear test, (6) decision rule. d. Are the test statistic F* and the decision rule for the general linear test numerically equivalent to those in part (a)?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 7E
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Please explain in detail thank you
Transcribed Image Text:A criminologist studying the relationship between level of education and crime rate in
a counties collected the following data for a random sample of 84 counties: X is the
percentage of individuals in the county having at least a high school diploma, and Y
is the crime rate (crimes reported per 100,000 residents) last year. Assume that first
order regression model Y₁ = ẞo + B₁X; + &; i = 1, 2, ..., 84 is appropriate.
a. Test whether or not there is a linear association between crime rate and percentage
of high school graduates, using a t test with a = 0.01. State the alternatives, decision
rule, and conclusion. What is the P-value of the test?
b. Suppose that the test in part (a) is to be carried out by means of a general linear test.
State the full and reduced models.
c. Obtain (1) SSE(F), (2) SSE(R), (3) dff, (4) dfR, (5) test statistic F* for the general
linear test, (6) decision rule.
d. Are the test statistic F* and the decision rule for the general linear test numerically
equivalent to those in part (a)?
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