A researcher wishes to determine if female students and male students differ in the size of their network of friends. She selects random samples of 10 female and 15 male students. Descriptive statistics are given below:
$n_{female}$ = 10 $\quad$ $\overline{x}_{female}$= 23 $\quad$ $s_{female}$ = 7.8
$n_{male}$ = 15 $\quad$ $\overline{x}_{male}$= 16 $\quad$ $s_{male}$ = 6.4
What is the standard error for the sampling distribution of $\overline{x}_{female}$ - $\overline{x}_{male}$ ?
A) 1.10
B) 8.81
C) 2.97
D) 7.10

Question

Quizplus · Accepted Answer

The standard error for the difference between two means is calculated using the formula: $\sqrt{\frac{s_{female}^2}{n_{female}} + \frac{s_{male}^2}{n_{male}}}$. Plugging in the given values, we get $\sqrt{\frac{7.8^2}{10} + \frac{6.4^2}{15}} = \sqrt{6.048 + 2.7392} = \sqrt{8.7872} \approx 2.97$.

A Researcher Wishes to Determine If Female Students and Male nfemalen_{female}nfemale​

A Researcher Wishes to Determine If Female Students and Male $n_{female}$