Data were collected on annual personal time (in hours) taken by a random sample of 16 women and 7 men employed by a medium sized company.The women took an average of 24.75 hours of personal time per year with a standard deviation of 2.84 hours.The men took an average of 21.89 hours of personal time per year with a standard deviation of 3.29 hours.The standard error of the sampling distribution for the difference between the two means is ________________________ .
A)2.05
B)5.02
C)2.24
D)1.43
E)0.48

Question

Quizplus · Accepted Answer

The standard error of the sampling distribution for the difference between two means can be 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. For the women: $s_1 = 2.84$, $n_1 = 16$; for the men: $s_2 = 3.29$, $n_2 = 7$. Plugging these values into the formula gives: $\sqrt{\frac{2.84^2}{16} + \frac{3.29^2}{7}} = \sqrt{\frac{8.0656}{16} + \frac{10.8241}{7}} = \sqrt{0.5041 + 1.5463} = \sqrt{2.0504} \approx 1.43$.

Data Were Collected on Annual Personal Time (In Hours) Taken