What is the test value? Use $a = 0.05$ . (Use the variances unequal formula.)
A) -6.97
B) -2.50
C) -4.53
D) -2.54

Question

Quizplus · Accepted Answer

To determine the test value, we need to use the formula:
t = (x̄1 – x̄2) / [s1²/n1 + s2²/n2]^(1/2)
Where x̄1 and x̄2 are the sample means, s1² and s2² are the sample variances, and n1 and n2 are the sample sizes.

Given the data:
x̄1 = 9.75
x̄2 = 14.25
s1² = 4.16
s2² = 6.25
n1 = 6
n2 = 8
α = 0.05

Substituting the values,
t = (9.75 – 14.25) / [4.16/6 + 6.25/8]^(1/2)
t = -2.54

Using a t-distribution table with (n1 + n2 - 2) degrees of freedom at α = 0.05 level of significance, we find the critical value to be ±2.306.

Since -2.54 < -2.306, we reject the null hypothesis and conclude that there is a significant difference between the mean scores of the two groups. Therefore, the best choice is D.

What Is the Test Value? Use a=0.05a = 0.05a=0.05 (Use the Variances Unequal Formula

What Is the Test Value? Use $a = 0.05$ (Use the Variances Unequal Formula