Question

In order to use a 90% confidence interval to compare admission exam scores for sophomores (group #1) and freshmen (group #2), two independent random samples were selected. The results showed:

1-Sophomores: Sample mean = 85, sample standard deviation = 10, sample size = 50.

2-Freshmen: Sample mean = 78, sample standard deviation = 12, sample size = 72.

A) For forming a 90% confidence interval for μ 1 − μ 2, the standard error is __________ .

B) For forming a 90% confidence interval for μ 1 − μ 2, the estimate is __________ .

C) For forming a 90% confidence interval for μ 1 − μ 2, the multiplier is __________ .

Answer 1

= 85 , S1=10, n1 =50

= 78 , S1=12 , n2 = 72

population standard deviation is estimated by pooled standard deviation.

= Sp = pooled standard deviation

Pooled variance,

Sp2 = ( (n1-1) S1 2 + (n2-1) S2 2 ) / (n1+n2-2)

=( 49* 10*10 + 71 * 12 * 12 ) / 120

= 126

Sp = 11.23

A) Standard error = Sp = 11.23 * = 2.067

B) I guess estimate means - = 85 -78 =7

C)Multiplier = t/2=0.05,120 = 1.660

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