Two random samples are selected from two independent populations. A summary of the samples sizes, sample...

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Two random samples are selected from two independent populations. A summary of the samples sizes, sample...

Two random samples are selected from two independent populations. A summary of the samples sizes, sample means, and sample standard deviations is given below:

n1= 37 n2=44

x-bar1= 58.6 x-bar2= 73.8

s1=5.4 s2=10.6

Find a 97% confidence interval for the difference μ1−μ2μ1−μ2 of the means, assuming equal population variances.

math Statistics-And-Probability

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Answer 1

Answer #1

The standard error here is computed as:

Now for n1 + n2 - 2 = 79 degrees of freedom, we get from the t distribution tables here:

P( t79 < 2.210) = 0.985,
Therefore, due to symmetry, we get here:
P( -2.210 < t79 < 2.210) = 0.97

The 97% confidence interval therefore is obtained here as:

This is the required 97% confidence interval for the difference in 2 population means here.

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Answer 2

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