## MS Mod 7 Difference of means for small samples practice exam questions...

 Author Message NEAS Supreme Being Group: Administrators Posts: 4.2K, Visits: 1.2K MS Module 7 Difference of means for small samples practice exam questions(The attached PDF file has better formatting.) Samples from two groups have the following samples sizes, means, and standard deviations: Group    Sample Size    Sample Mean    Sample SDGroup 1    5    12    1.1Group 2    7    15    1.4μ1 = the mean of Group #1; μ2 = the mean of Group #2.The null hypothesis is H0: μ1 = μ2; the alternative hypothesis is Ha: μ1 ≠ μ2.Question 7.1: Variance of estimated meanWhat is the variance of the estimated mean of each group?Answer 7.1: variance of the estimated mean = (standard deviation)2 / number of observations●    Group 1: 1.12 / 5 = 0.242●    Group 2: 1.42 / 7 = 0.280Question 7.2: Variance of estimated difference of group meansWhat is the variance of the estimated difference of the group means?Answer 7.2: 0.242 + 0.280 = 0.522(variance of the estimated difference of the group means = sum of variances of estimated group means)Question 7.3: Standard deviation of estimated difference of group meansWhat is the standard deviation of the estimated difference of the group means?Answer 7.3: 0.5220.5 = 0.7225(standard deviation = square root of the variance)Question 7.4: Degrees of freedom What are the degrees of freedom for a t test of each group’s mean?Answer 7.4: Degrees of freedom = number of observations – 1●    Group 1: 5 – 1 = 4●    Group 2: 7 – 1 = 6Question 7.5: Degrees of freedomWhat are the degrees of freedom for a t test of the difference of the group means?Answer 7.5: The approximate degrees of freedom is(s21/m + s22/n)2 / (s21/m)2/(m-1) + (s22/n)2/(n-1) =(variance of group 1 mean + variance of group 1 mean)2 /    (square of variance of group 1 mean / (group 1 observations – 1) +    square of variance of group 2 mean / (group 2 observations – 1) ) =     (0.242 + 0.280)2 / (0.2422 / (5 – 1) + 0.282 / (7 – 1) ) = 9.834We truncate the degrees of freedom to 9.Question 7.6: t value for difference of group meansWhat is the t value for a 90% two-sided confidence interval of the difference of the group means?Answer 7.6: 1.833(the t value for a 90% two-sided confidence interval is the t value for a 5% one-tailed test with 9 degrees of freedom)Question 7.7: Confidence intervalWhat is the 90% two-sided confidence interval of the difference of the group means (μ1 – μ2)?Answer 7.7: Confidence interval = (μ1 – μ2) ± t value × standard deviation of the difference of the group means●    lower bound: (12 – 15) – 1.833 × 0.7225 = -4.324●    upper bound: (12 – 15) + 1.833 × 0.7225 = -1.676 Attachments MS Module 7 Difference of means for small samples practice exam questions.pdf (241 views, 48.00 KB)
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