two randomly assigned groups are compared in a health pilot evaluation project. data down on both...

two randomly assigned groups are compared in a health pilot evaluation project. data down on both groups are assumed to be normally distributed. the mean for the group 1 is 280, with a standard deviation of 15. the mean for group 2 is 230, with a standard deviation of 8. the number of observation for each group is 45. assume the level of significance is 5%. determine whether these two groups are statistically similar. show your hypothesis, calculated and critical t-values, decision and conclusion.

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Expert Solution

We have to test, H0: = against H1: .

and are the means of group 1 and group 2 respectively.

The test-statistic is, T = , where, = 280, = 230, = 15, = 8, = 45, = 45

Thus, T = 19.73. Under H0, T ~ t-distribution with (45 + 45 -2) d.f. i.e. 88 d.f.

The critical values are and i.e. and = - 1.987 and 1.987.

Since, T = 19.73 > 1.987, we reject H0.

There is enough evidence to conclude that the two groups are not statistically similar.

milcah answered 9 months ago

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