Statistical Analysis of Two Population Means: Hypothesis Testing and Confidence Intervals , Assignments of Mathematical Statistics

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a)H 0 : u=16.5 vs Ha: u>16.5 , where n=200, mean=17.05 , S=5. b) P-value=.068 , at ά =.05, we reject null hypothesis, at ά =.10, we accept null hypothesis. c) A two-tailed test is inappropriate because the alternative hypothesis is greater than 16.5, not unequal to 16.5.

Compare means of two populations, we use 2-sample t test H 0 : u 1 = u2 vs Ha: u 1 ≠ u 2 , at ά =. Pooled standard deviation: S^2 =60.526, Use formula at text page 491, we get t=.29< t (^) ά =.025 , v Note: v is degree of freedom calculated from text page 492 Conclusion: we can’t reject null hypothesis, no trend exists.

a) 90% confidence interval is (3.59,4.21) b) H 0 : u 1 = u2 vs Ha: u 1 ≠ u Use formula at text page 491, t=20.6> t (^) ά =.005 , v Note: v is degree of freedom calculated from text page 492 Conclusion: we reject null hypothesis, two sample means are not equal. c) Assume n1=n2=n, we use formula at text page 522, n=

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