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
alphaα=0.01
level of significance for the given sample data.(b) Construct a
99%
confidence interval about
mu 1μ1minus−mu 2μ2.



Population 1

Population 2



n

24

25


x overbarx

50.8

45.9


s

4.3

11.4

Let fouryear colleges be the first sample and the twoyear colleges be the second sample.
Option E is correct.
Hypotheses for the test is given below:
This test is a righttailed test.
Test statistic for ttest:
Since population standard deviations are unknown, the appropriate test is two sample ttest.
Here, the sample means of 1^{st} and 2^{nd} samples are 50.8 and 45.9 respectively.
Sample standard deviations of 1^{st} and 2^{nd} samples are 4.3 and 11.4 respectively.
Sample size of 1^{st} and 2^{nd} samples are 24 and 25 respectively.
The pooled standard deviation can be calculated as follows:
The test statistic for ttest is calculated as given below.
The value of test statistic is 2.5.
Computation of Pvalue:
The right tailed Pvalue for the ttest at 47 degrees of freedom is approximately 0.025 whi...
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