# Variance & Linear Regression

Need help with examples attached.

There is a comment in two cells that have a formula for hypotheses...I did not know how to place the digits directly above / under each other.

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#1 The following hypotheses are given:

H0: σ21 = σ22

H1: σ21 ≠ σ22

A random sample of eight observations from the first population resulted in a standard deviation of 10.

A random sample of six observations from the second population resulted in a standard deviation of 7.

At the .02 significance level, is there a difference in he variation of the two populaions?

#2 given the following sample information tests the hypothesis that the treatment means are equal at the .05 significance level.

Treatment1 Treatment 2 Treatment 3

8 3 3

11 2 4

10 1 5

3 4

2

a. State the null hypothesis and the alternate hypothesis.

b. What is the decision rule?

C. Compute SST, SSE, and SS total

d. Complete an ANOVA table

e. State your decision regarding the null hypothesis.

F. if H0 is rejected, can we conclude that treatment 1 and 2 differ? Use the 95 percept level of confidence.

#3 the city council of Pine Bluffs is considering increasing the number of police in an effort to reduce crime.

Before making a final decision, the council asks the Chief of Police to survey other cites of similar size to

Determine the relationship between the number of police and the number of crimes reported.

The Chief gathered the following sample information.

City Police # of Crimes City

Oxford 15 17 Holgate

Starkville 17 13 Carey

Danville 25 5 Whistler

Athens 27 7 Woodville

a. If we want to estimate crimes on the basis of the number of police, which variable is the dependent variable and

Which is the independent variable?

b. Draw a scatter diagram

c. Determine the coefficient of correlation

d. Determine the coefficient of determination

e. Interpret these statistical measures. Does it surprise you that the relationship is inverse?

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#### Solution Preview

Please see attached Word document for solutions and explanations.

#1 The following hypotheses are given:

H0: σ21 = σ22

H1: σ21 ≠ σ22

A random sample of eight observations from the first population resulted in a standard deviation of 10.

A random sample of six observations from the second population resulted in a standard deviation of 7.

At the .02 significance level, is there a difference in he variation of the two populations?

Compute the test stats:

Use a website http://duke.usask.ca/~rbaker/Tables.html or your book to get p-value = 0.2249 > 0.02.

So, we conclude that at the .02 significance level, there is no difference in the variation of the two populations.

#2 Given the following sample information, test the hypothesis that the treatment means are equal at the .05 significance level.

Treatment1 Treatment 2 Treatment 3

8 3 3

11 2 4

10 1 5

3 4

2

a. State the null hypothesis and the alternate hypothesis.

b. What is the decision rule?

c. Compute SST, SSE, and SS total

d. Complete an ANOVA table

e. State your decision regarding the null hypothesis.

f. if H0 is rejected, can we conclude that treatment 1 and 2 differ? Use the 95 percent level of confidence.

a. State the null hypothesis and the alternate hypothesis.

Null hypothesis H0: the ...

#### Solution Summary

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