7. The following two data sets contain random sample of test scores for 15 boys

Question

7. The following two data sets contain random sample of test scores for 15 boys (set A) set A (x): L3 = {81, 87, 67, 69, 90, 90, 70, 75, 83, 65, 78, 76, 91, 69, 83) set B (x2) L4 (71,94, 68, 89, 70, 84, 79, 85, 53, 65,98, 75,91, 67, 79) and 15 girls (set B): Using 2-SampTInt on your calculator, find (i) the point estimate of the difference between the mean score for boys and for girls, (ii) the 99% confidence interval estimate of the difference, and (ii) the margin of error. sample statistic x, a2- 98% confidence interval (round to the tenths, place): margin of error

Explanation / Answer

Sample statistics, mu1 = 78.26667

                           mu2 = 77.866666666667

The formula for estimation is:

1 - 2 = (M1 - M2) ± ts(M1 - M2)

where:

M1 & M2 = sample means
t = t statistic determined by confidence level
s(M1 - M2) = standard error = ((s2p/n1) + (s2p/n2))

Calculation

Pooled Variance
s2p = (SS1 + SS2) / (df1 + df2) = 235.33 / 28 = 8.4

Standard Error
s(M1 - M2) = ((s2p/n1) + (s2p/n2)) = ((8.4/15) + (8.4/15)) = 1.06

Confidence Interval
1 - 2 = (M1 - M2) ± ts(M1 - M2) = 0.4 ± (2.47 * 1.06) = 0.4 ± 2.6182

Result

1 - 2 = (M1 - M2) = 0.4, 98% CI [-2.2182, 3.0182].

You can be 95% confident that the difference between your two population means (1 - 2) lies between -2.22 and 3.02.

Margin of error = 1.06

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