Use the given statistics to complete parts (a) and (b). Assume that the populations are normally distributed.
(a) Test whether
mu 1μ1greater than>mu 2μ2
at the
alphaαequals=0.05
level of significance for the given sample data.(b) Construct a
90%
confidence interval about
mu 1μ1minus−mu 2μ2.



Population 1

Population 2



n

26

21


x overbarx

47.2

40.5


s

4.6

11.8

Hypotheses for the test is given below:
The correct answer is option E.
This test is a righttailed test.
Test statistic for ttest:
Since population standard deviations are unknown, the appropriate test is two sample ttest.
Here, Sample sizes of 1^{st} and 2^{nd} samples are 26 and 21 respectively.
The sample means of 1^{st} and 2^{nd} samples are 47.2 and 40.5 respectively.
Sample standard deviations of 1^{st} and 2^{nd} samples are 4.6 and 11.8 respectively.
The pooled standard deviation can be calculated as follows:
The test statistic for ttest is cal...
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