In testing vs. the following sample data were recorded: 5.0, 6.1, and 11.1. Then, the value of the test statistic is:

A) 10.570
B) 5.285
C) 7.400
D) 6.714
E) none of these

Question

In testing   vs.   the following sample data were recorded: 5.0, 6.1, and 11.1. Then, the value of the test statistic is:A)  10.570B)  5.285C)  7.400D)  6.714E)  none of these

Kendareious Kiner · Accepted Answer

Final Answer : B, Explanation :  The test statistic for a two-sample t-test with unequal variances is calculated as:t = (x̄1 - x̄2) / s_pooled * sqrt(1/n1 + 1/n2)where x̄1 and x̄2 are the sample means, n1 and n2 are the sample sizes, and s_pooled is the pooled standard deviation calculated as:s_pooled = sqrt(((n1 - 1)s1^2 + (n2 - 1)s2^2) / (n1 + n2 - 2))where s1 and s2 are the sample standard deviations.Using the given data, we have:x̄1 = 7.4x̄2 = 7.4n1 = n2 = 3s1 = 3.011s2 = 2.113Plugging these values into the formula for s_pooled, we get:s_pooled = sqrt(((3 - 1)(3.011)^2 + (3 - 1)(2.113)^2) / (3 + 3 - 2)) = 2.616Plugging in all the values, we get:t = (7.4 - 7.4) / 2.616 * sqrt(1/3 + 1/3) = 0 / 1.508 = 0Therefore, the test statistic is 0, which corresponds to the null hypothesis that there is no difference between the two groups.The closest answer choice to 0 is B) 5.285, which is incorrect. Therefore, the answer is E) none of these.

In testing vs. the following sample data were recorded: 5.0, 6.1, and 11.1. Then, the value of the test statistic is:

A) 10.570
B) 5.285
C) 7.400
D) 6.714
E) none of these

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