The head circumference is measured for a sample of 17 girls and a separate sample of 12 boys. The mean for the girls was 49 cm with a standard deviation of 1.25 cm. The mean for the boys was 50 cm with a standard deviation of 0.95 cm. What is the value of the pooled standard error for the difference in mean head circumference between girls and boys?
A) 0.41
B) 1.29
C) 0.43
D) 1.14

Question

Quizplus · Accepted Answer

The pooled standard error (SE) for the difference between two means can be calculated using the formula: $$SE = \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$$ where $s_1$ and $s_2$ are the standard deviations of the two samples, and $n_1$ and $n_2$ are the sample sizes. Plugging in the given values: $$SE = \sqrt{\frac{1.25^2}{17} + \frac{0.95^2}{12}} = \sqrt{\frac{1.5625}{17} + \frac{0.9025}{12}} = \sqrt{0.0919117647 + 0.0752083333} = \sqrt{0.167120098} \approx 0.409}$$ Therefore, the closest value provided is 0.43.

The Head Circumference Is Measured for a Sample of 17