Question

A randomly selected sample of 60 mathematics majors spent an average of $200.00 for textbooks one term, while during the same term, a randomly selected sample of 40 literature majors spent an average of $180.00 for textbooks.

The standard deviation for each sample was $20.00. The standard error for the difference between the two sample means is:
A. 0.057
B. 4.082
C. 5.744
D. 16.663

Answer 1

c. 5.744

Explanation:

given the following:

N1,population sample 1= 60 mathematics majors

average mean 1 =$200.00 for textbooks

N2' POPulation sample 2 = 40 literature majors

average mean 2 = $180.00 for textbooks.

The standard deviation,ρ for each population sample = $20.00.

to calculate the standard error, we will use the formula

standard error SE = standard deviation / root population

SE for sample 1 = ρ/root N1

= 20/ root 60 = 2.58

SE for sample 1 = ρ/root N2

SE for sample 2= 20/root40 = 3.162

The standard error for the difference between the two sample = adding SE1 + SE2

= 2.58 + 3.162 = 5.744

Answer 2

Option B is correct = 4.082

Explanation:

From the question, we have the following information;

Sample A, 60 people are randomly selected = $200 for textbook in one term.

Sample B:, 40 people are randomly selected = $180 for textbook in one term. Standard deviation of sample A and B =$20.

Difference in the average value= 200-180 = 20.

To calculate the standard error we have;

Standard error= SD/√number of sample.

Standard error= 20/√20 = 20/ 4.472

= 4...