A randomly selected sample of 60 mathematics majors spent an average of $200.00 for textbooks one term, while during the same term, a randomly selected sample of 40 literature majors spent an average of $180.00 for textbooks. The standard deviation for each sample was $20.00. The standard error for the difference between the two sample means is
A) 0.057
B) 4.082
C) 5.744
D) 16.663

Question

Quizplus · Accepted Answer

The standard error for the difference between two sample means is calculated using the formula: $\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$, where $s_1$ and $s_2$ are the standard deviations of the two samples, and $n_1$ and $n_2$ are the sample sizes. Substituting the given values ($s_1 = s_2 = 20$, $n_1 = 60$, $n_2 = 40$), we get $\sqrt{\frac{20^2}{60} + \frac{20^2}{40}} = \sqrt{\frac{400}{60} + \frac{400}{40}} = \sqrt{6.67 + 10} = \sqrt{16.67} \approx 4.082$.

A Randomly Selected Sample of 60 Mathematics Majors Spent an Average