Fissd tom on the value acinted wls comsider the llowing talle of sutamary statis
ID: 3309444 • Letter: F
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Fissd tom on the value acinted wls comsider the llowing talle of sutamary statislics poofed estima associated Sumple Sample mean Mandard devlation 1156.5 132.6 26.5 21.5 robust Two -0 versus a. Conduct a hypothesis test of Ho: 1-2 e the popula- tatistics onfidence variances r of earest b. Find bounds on the p value associated with this test. 10.39 Given the two sample r test assumpt the independent random samples from two different populations. EX1039 a. Conductahypothesis test of Ho: -Ha-0 versus b. Find bounds on the p value associated with this test. 10.40 Given the two-sample test assumptions, consider the interval following table of summary statistics. heans Sample Sample Sample Group size mean standard deviation One Two 9.24 8.15 23 23 49.03 the 49.57 a. Find a 95% confidence interval for the difference in b. Using the confidence interval in part (a), is there any population means, 1-2. evidence to suggest that the two population means are different? Justify your answerExplanation / Answer
10.40
The standard error (SE) of the sampling distribution is
SE = sqrt[ (s12/n1) + (s22/n2) ]
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.
SE = sqrt[ (9.242/23) + (8.152/23) ] = 2.569
The degrees of freedom (DF) is:
DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] }
DF = (9.242/23 + 8.152/23)2 / { [ (9.242 / 23)2 / (23 - 1) ] + [ (8.152 / 23)2 / (23 - 1) ] }
= 43 (Rounded to nearest integer)
t value for 95% confidence inetrval and df = 43 is 2.0167
Difference in means = 49.03 - 49.57 = -0.54
Margin of error = t * SE = 2.0167 * 2.569 = 5.181
95% confidence interval is,
(Difference in means - Margin of error, Difference in means + Margin of error)
(-0.54 - 5.181, -0.54 + 5.181)
= (-5.721, 4.641)
b.
As, the 95% confidence interval contains 0, so, there is evidence to suggest that the difference in means is 0. In other words, there is evidence that the two population means are equal. There is no evidence that the two population means are different.
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