Hypothesis testing for two populations (unpaired and paired tests)•Testing the difference between the means for unpaired samples•Sampling distribution of (large sample)•Wrap up of cases for unpaired testing•Testing the difference between the variance of two populations•Sampling distribution of •Testing the difference between means for paired samples21XX22222121SS

EXAMPLEThe placekicker on a university football team notices that he seems to kick the ball farther when the weather is warm compared to when it is cold. To investigate, the kicker decides to do an experiment, to see if the football can be kicked farther after it has been heated compared to when it is cold From an initial pool of 60 kickers and 60 footballs (30 cold and 30 heated):He randomly assigns 30 kickers to kick 30 cold footballsHe then randomly assigns 30 other kickers to kick 30 heated footballsIn this situation all the kicks are independent from each otherTESTING THE DIFFERENCE BETWEEN THE MEANS OF TWO POPULATIONS (UNPAIRED TESTS)

CONDITIONS OF THE EXPERIMENT IN THE EXAMPLE•Random samples are taken from both populations•Both samples are independently taken•Both samples can be assumed normally distributed TESTING THE DIFFERENCE BETWEEN THE MEANS OF TWO POPULATIONS (UNPAIRED TESTS)

Two tailed testTESTING THE DIFFERENCE BETWEEN THE MEANS OF TWO POPULATIONS (UNPAIRED TESTS)Left tailed testRight tailed test0210210::DHDHa0210210::DHDHa0210210::DHDHa

LARGE SAMPLE CASEIn the large sample case, the estimator has an approximate normal distribution.Hence, for testing , , we can use the following test statistic: SAMPLING DISTRIBUTION OF 21XX21XX222121021nSnSDXXZ021:DHa021:DHa021:DHa

Can the football be kicked farther after it has been heated?