Question

please answer both of the following:

1.

Exhibit 10-3
A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. Final examination scores from a random sample of students enrolled today and from a random sample of students enrolled five years ago were selected. You are given the following information.

	Today	Five Years Ago
	82	88
σ2	112.5	54
n	45	36

Refer to Exhibit 10-3. The standard error of  is _____.

A: 12.9

B: 9.3

C: 4

D: 2

2.

Exhibit 10-3
A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. Final examination scores from a random sample of students enrolled today and from a random sample of students enrolled five years ago were selected. You are given the following information.

	Today	Five Years Ago
	82	88
σ2	112.5	54
n	45	36

Refer to Exhibit 10-3. The 95% confidence interval for the difference between the two population means is _____.

A: -9.92 to -2.08

B: -3.92 to 3.92

C: -13.84 to 1.84

D: -24.228 to 12.23

Answer 1

10.3)

Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(112.49996356/45 + 54.00045225/36)
sp = 2

standard error = 2

2)

Given CI level is 0.95, hence α = 1 - 0.95 = 0.05                  
α/2 = 0.05/2 = 0.025, zc = z(α/2, df) = 1.96                  
                  
Margin of Error                  
ME = zc * sp                  
ME = 1.96 * 2                  
ME = 3.92                  
                  
CI = (x1bar - x2bar - tc * sp , x1bar - x2bar + tc * sp)                  
CI = (82 - 88 - 1.96 * 2 , 82 - 88 - 1.96 * 2                  
CI = (-9.92 , -2.08)                  
           A: -9.92 to -2.08