Question

A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are µ = 3.5 and σ = 0.5. Suppose a random sample of 100 male students is selected and the GPA for each student is calculated. Find the interval that contains 95.44 percent of the sample means for male students.

[3.45, 3.55]

[2.50, 4.50]

[3.35, 3.65]

[3.40, 3.60]

Answer 1

Here we  assume the population mean and standard deviation for the GPA of male students are µ = 3.5 and σ = 0.5.

n = 100 which is very large so we can use central limit theorem.

The standard deviation of sample mean is as follow:

Here we want to find lower limit (LL) and upper limit (UL) such that P( LL < < UL ) = 0.9544

this implies

P( < LL ) = (1 - 0.9544)/2 = 0.0228

and P( < UL ) = 1 - 0.0228 = 0.9772

Let's use excel to find LL and UL:

LL = "=NORMINV(0.0228,3.5,0.05)" = 3.40

UL = "=NORMINV((0.9772),3.5,0.05)" = 3.60

So correct choice is D) [3.40, 3.60]