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

Quizplus · Accepted Answer

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 = 7.4
x̄2 = 7.4
n1 = n2 = 3
s1 = 3.011
s2 = 2.113

Plugging 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)) = 2.616

Plugging in all the values, we get:

t = (7.4 - 7.4) / 2.616 * sqrt(1/3 + 1/3) = 0 / 1.508 = 0

Therefore, 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