Question

Your professor wants to determine if her students today are performing better in statistics than 10 years ago. End of semester grades from a random sample of students enrolled today and one of students enrolled 10 years ago have been obtained:
Today 10 Years Ago
82 88
σ 2 112.5 54
n 45 36
The test statistic for the difference between the two population means is _____.
a) –3
b) –1.5
c) –.65
d) –.47

Answer 1

Answer:

z = -3

Step-by-step explanation:

If we had two independent samples, the variance is known and $n_1$ and $n_2$ are bigger than 30, the test statistic for the difference between the two population means is calculated as:

$z=\frac{x_1-x_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} } }$

Where $x_1$ and $x_2$ are the means of the samples, $s_1^2$ and $s_2^2$ are the variances of the samples and $n_1$ and $n_2$ are the size of the sample.

Finally, replacing  $x_1$ by 82, $x_2$ by 88, $s_1^2$ by 112.5 , $s_2^2$ by 54, $n_1$ by 45 and $n_2$ by 36, we get that the statistic is equal to:

$z=\frac{82-88}{\sqrt{\frac{112.5}{45}+\frac{54}{36} } }=-3$