Question

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. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. Today Five Years Ago x̄ 82 88 σ2 112.5 54 n 45 36

The 95% confidence interval for the difference between the two population means is

a. -3.08 to 3.92.

b. -9.92 to -2.08.

c. -13.84 to -1.16.

d. -24.77 to 12.23

Answer 1

SOLUTION:

From given data,

x̄	= 82	= 88
σ2	= 112.5	=54
n	=45	= 36

95% confidence interval

Confidence interval is 95%

95% = 95/100 = 0.95

= 1 - Confidence interval = 1-0.95 = 0.05

/2 = 0.05 / 2

= 0.025

Z_/2 = Z_0.025 = 1.96

The 95% confidence interval for the difference between the two population means is

95% CI = (-) Z_/2 * sqrt( / + / )

95% CI = (82-88) 1.96 * sqrt(112.5/45  + 54/ 36)

95% CI = -6 1.96 * 2

95% CI = -6 3.92

-6 - 3.92 <  - < -6 + 3.92

-9.92 <  - < -2.08

Answer : Option(b) is correct

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