# OSU BUSMGT 2320 - Comparisons of Two Populations (mu) Additional Practice Solutions (9 pages)

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## Comparisons of Two Populations (mu) Additional Practice Solutions

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- Pages:
- 9
- School:
- Ohio State University
- Course:
- Busmgt 2320 - Decision Sciences: Statistical Techniques

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Comparisons Additional Practice Problems Solutions 1 If some natural relationship exists between each pair of observations that provides a logical reason to compare the first observation of sample 1 with the first observation of sample 2 the second observation of sample 1 with the second observation of sample 2 and so on the samples are referred to as a matched samples definition b independent samples c weighted samples d random samples 2 True or False A researcher is curious about the effect of sleep on students test performances He chooses 50 students and gives each two tests one given after four hours of sleep and one after eight hours of sleep The test the researcher should use would be matched pairs t test Each student is measured twice A student s general understanding of the subject matter analytical skills etc will remain the same for both tests 3 Consider the following hypothesis test Ho 1 2 1 7 n1 20 X 1 25 2 H1 1 2 1 7 n2 35 X 2 20 4 s1 4 0 05 s2 7 a What is the appropriate test statistic Z or t If t also indicate the degrees of freedom s22 49 Use the Satterthwaite Approximation Method since 2 3 0625 2 s1 16 x x 2 1 2 The test statistic is t obs 1 t 52 s12 s22 n1 n2 2 16 49 20 35 df 52 99 Use 52 df 2 2 2 2 2 2 16 49 s1 s2 n n 20 35 1 2 16 1 35 1 n1 1 n2 1 s12 s22 n 1 n2 2 Note If you do not have access to statistical computing software and the calculation of is not reasonable substitute the smaller of n1 1 and n2 1 for the df In this case you would substitute 19 This is far fewer df than the actual 52 so use if possible b What are the value s of the critical point s Express your answer to 3 decimal places The value will depend on access to computer or printed table If using printed table and df are not in table use next lower available df I m using df 40 t criticals t with 52 df row and 0 025 tail area column t criticals 2 021 c What is the 95 Confidence Interval estimate of 1 2 Express your answer to 3 decimal places X 1 X 2 t s12 s 22 16 49 25 2 20 4 2

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