Previous Problem List Next (2 points) Test the claim that the two samples descri

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Previous Problem List Next (2 points) Test the claim that the two samples described below come from populations with the same mean. Assume that the samples are independent random samples, the populations are normal, and that population variances are equal Sample 1: n1 = 10, zi = 14, 81-2.5. Sample 2:n,-13, 12, 82 = 1 (a) The test statistic is (b) Find the t critical value for a significance level of 0.01 for an alternative hypothesis that the first population has a LARGER mean (one-sided test): to = (c) The conclusion is OA. There is sufficient evidence to warrant rejection of the claim that the two populations have the same mean and support that the first population has a larger mean. B. There is not sufficient evidence to warrant rejection of the claim that the two populations have the same mean. Note: You can earn partial credit on this problem. You have attempted this problem 0 times.

Explanation / Answer

Solution:

From the given information
n1 = 10, x1 = 14, s1 = 2.5
n2 = 13, x2 = 12, s2 = 1
SE = sqrt[(s1^2/n1)+ (s2^2/n2)]
= sqrt[(2.5^2/10) + (1^2/13)]
= 0.8378
a) The test statistic t = [ (x1 - x2) / SE ]
= [ (14-12) / 0.8378]
= 2.3872
Degree of freedom = n1 + n2 - 2 = 10 + 13 -2 = 21
b) Critical value of t at 0.01 significance level
P(t > 2.39) = 0.00001

c) Since p value is < 0.01

There is sufficient evidence to warrant rejection of the claim that the two populations have the same mean and accept that the first population has a larger mean.

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