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

z = -3

Step-by-step explanation:

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

Where and are the means of the samples, and are the variances of the samples and and are the size of the sample.

Finally, replacing   by 82, by 88, by 112.5 , by 54, by 45 and by 36, we get that the statistic is equal to: