Question

Population 1 Poulation 2 n 28 15 x 46.7 42.5 s 4.8 13.1 Use the given statistics to complete parts​ (a) and​ (b). Assume that the populations are normally distributed. ​(a) Test whether μ1>μ2 at the alpha=0.01 level of significance for the given sample data.​ (b) Construct a 95​% confidence interval about μ1−μ2.

Answer 1

a) = 1% = 0.01

Hypothesis:

Ho: 1 = 2

Ha: 1 > 2

First We need to find out, Degrees of Freedom

Degrees of Freedom:

Test statistic:

Critical value:

...............Using t table

Conclusion:

Test statistic < Critical value, 1.20 < 2.5835, That is Fail to Reject Ho at 1% level of significance.

b)

Critical value:

..............Using t table

95% Confidence Interval:

(-3.22, 11.62) OR -3.22 <  1-2 < 11.62

Here, Population mean difference = 0 i,e, 1-2= 0, Is included in this interval

That is, Fail to Reject Ho at 5% level of significance.