We are interested in determining if there is any difference in the test scores o

Question

We are interested in determining if there is any difference in the test scores of students registered in major A and major B. To test this hypothesis we take a sample of students from both majors and get the following information.

Sample Major A

Sample Major B

Sample Mean

76

84

Sample Variance

85

80

Sample Size

20

22

1) The standard error of the difference in sample means is? A) 2.8, B) 4.6, C) 4.99, D) 10.8

2) The degrees of freedom for the t-distribution are (use the simplification formula): A) 19, B) 21, C) 22, D) 34

3) The 95% confidence interval for the difference between the two population means is? A) 20.6 to 4.6, B) -15.56 to -.44, C) -12.5 to -3.5, D) -14 to -2

Sample Major A

Sample Major B

Sample Mean

76

84

Sample Variance

85

80

Sample Size

20

22

Explanation / Answer

q1) Standard error of the difference in sample means = Sqrt((85/20)+(80/22)) = 2.8

Option A is Correct

Q2) Degree of freedom = Min(20-1, 22-1) = 19

Option A is Correct

Q3) Margin of error = 2.093*2.8 = 5.888

95% Interval

(76-84-5.888, 76-84+5.888)

= (-14, -2)

Option D is Correct

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