Random samples that are drawn independently from two normally distributed popula

Question

Random samples that are drawn independently from two normally distributed populations yielded the following statistics. Group 1 Group 2 (The first row gives the sample sizes, the second row gives the sample means, and the third row gives the sample variances.) Can we conclude, at the significance level, that the population variance, , for group 1 is greater than the population variance, , for group 2? Perform a one-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic:The value of the test statistic: (Round to at least three decimal places.) The p-value: (Round to at least three decimal places.) Can we conclude that the population variance for group 1 is greater than the population variance for group 2?YesNo

Question #6 / 10

Perform a one-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

The null hypothesis:

H0:

The alternative hypothesis:

H1:

The type of test statistic:

(Choose one)ZtChi squareF

The value of the test statistic:
(Round to at least three decimal places.)

The p-value:
(Round to at least three decimal places.)

Can we conclude that the population variance for group 1 is greater than the population variance for group 2?

Yes

No

p

x

s

p

Question #6 / 10

   Random samples that are drawn independently from two normally distributed populations yielded the following statistics. Group 1 Group 2 (The first row gives the sample sizes, the second row gives the sample means, and the third row gives the sample variances.)

Can we conclude, at the significance level, that the population variance, , for group 1 is greater than the population variance, , for group 2?

Perform a one-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

n1=14

Explanation / Answer

Data:      

n1 = 14     

n2 = 19     

s1^2 = 888.04     

s2^2 = 428.49     

Hypotheses:     

Ho: 1^2 = 2^2     

Ha: 1^2 > 2^2     

Decision Rule:     

= 0.05     

Numerator DOF = 14 - 1 = 13   

Denominator DOF = 19 - 1 = 18   

Critical F- score = 2.314304    

Reject Ho if F > 2.314304    

Test Statistic:     

F = s1^2 / s2^2 = 888.04/428.49 = 2.0725   

p- value = 0.075932     

Decision (in terms of the hypotheses):   

Since 2.072487 < 2.3143 we fail to reject Ho

Conclusion (in terms of the problem):   

There is no sufficient evidence that 1^2 > 2^2

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