Suppose you used a 9-point rating scale to compare men who had an annual income over $50 000 (Group 1) with men who had an annual income less than or equal to $50 000 (Group 2) on their liking of a new product. If you studied 40 men in Group 1 and they had a mean of 7 and a standard deviation of 2.5, while the 35 men in Group 2 had a mean of 5 and a standard deviation of 1.4, what is the approximate value of using the t-test?
A) 8.78
B) 4.19
C) 0.97
D) 0.47

Question

Quizplus · Accepted Answer

The t-test value can be calculated using the formula for the independent samples t-test, which is: $t = \frac{\bar{X}_1 - \bar{X}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}$, where $\bar{X}_1$ and $\bar{X}_2$ are the sample means, $s_1^2$ and $s_2^2$ are the sample variances, and $n_1$ and $n_2$ are the sample sizes for groups 1 and 2, respectively. Plugging in the given values ($\bar{X}_1 = 7$, $s_1 = 2.5$, $n_1 = 40$, $\bar{X}_2 = 5$, $s_2 = 1.4$, $n_2 = 35$), the calculation yields a t-value close to 4.19, making choice B the correct answer.

Suppose You Used a 9-Point Rating Scale to Compare Men