Boys and girls have a lot in common, but they also seem to have a lot of differences. Some people have argued that, even at a young age, girls are more nurturing and caring than boys. Others think this is just an unfounded stereotype. Suppose that you, as a developmental psychologist, decide to test this out. You select a random sample of 20 boys and 20 girls and measure their level of caring for a sad friend. Boys have a mean of 4.0 and a standard deviation of 1.0 on the nurturing scale. Girls have a mean of 4.5 and a standard deviation of 1.2 on the nurturing scale. Using an alpha level of .05, conduct the analysis to determine which hypothesis is supported.

Question

Quizplus · Accepted Answer

The Answer is X_b = 4.0, s_b = 1.0
Xg = 4.5, s_g = 1.2
df = 20 + 20 -2 = 38

\alpha

= .05
2-tailed
t_c= 1.69

\begin{array}{l}s_{\bar{x}-\mathrm{b}}=1 / \sqrt{20} ightarrow 1 / 4.47 ightarrow .22 \s_{\bar{x}-\mathrm{g}}=1.2 / \sqrt{20} ightarrow 1.2 / 4.47 ightarrow .27 \\s_{\bar{x} 1-\bar{x} 2}=\sqrt{ }(.22)^{2}+(.27)^{2} ightarrow \sqrt{ }(.048+.073) ightarrow \sqrt{.121} ightarrow .348 \\t_{o}=4.5-4.0 / .348 \t_{o}=.5 / .348 \t_{o}=1.44\end{array}

My observed t is smaller than my critical t. Therefore, I retain the null hypothesis and conclude that there are no differences between boys and girls in their level of caring for a sad friend in the populations.

Boys and Girls Have a Lot in Common, but They