Answer the following questions and use Excel or this document to show your work. 1. Consider...

Answer the following questions and use Excel or this document to show your work.

1. Consider the following results for two samples randomly taken from two normal populations with equal variances.

	Sample I	Sample II
Sample Size	28	35
Sample Mean	48	44
Population Standard Deviation	9	10

a. Develop a 95% confidence interval for the difference between the two population means.

b. Is there conclusive evidence that one population has a larger mean? Explain.

Solutions

Expert Solution

Part a)

Confidence interval :-

Z(α/2) = Z (0.05 /2) = 1.96

Lower Limit =
Lower Limit = -0.6998
Upper Limit =
Upper Limit = 8.6998
95% Confidence interval is ( -0.6998 , 8.6998 )

Part b)

To Test :-
H0 :- µ1 = µ2
H1 :- µ1 > µ2

Test Statistic :-

Z = 1.6681

Test Criteria :-
Reject null hypothesis if Z > Z(α)
Z(α) = Z( 0.05 ) = 1.64
Z > Z(α) = 1.6681 > 1.64
Result :- Reject Null Hypothesis

Decision based on P value
Reject null hypothesis if P value < α = 0.05 level of significance
P value = P ( Z < 1.6681 )
P value = 0.0476
Since 0.0476 < 0.05 ,hence we reject null hypothesis
Result :- Reject null hypothesis

There is sufficient evidence to support the claim that one population has a larger mean.

milcah answered 8 months ago

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