Question

Problem: The IQ test scores of 45 seventh-grade girls in a Midwest school district are below.

111      107      100      107      115      111      97        112      104            106      113      109      113      128      128

118      113      124      127      136      106      123      124      126            116      127      119      97        102      110

120      103      115      93        123      79        119      110      110            107      105      105      110      77        90

Here are the IQ test scores of 30 seventh-grade boys in the same school district. Is there good evidence that girls and boys differ in their mean IQ scores?

114      100      104      89        102      91        114      114      103            105      108      130      120      132      111

128      118      119      86        72        111      103      74        112            107      103      98        96        112      112

Compute a 95% confidence interval for the difference between seventh-grade girls and boys IQs. Interpret. Also, at 5% significance level what is the p-value and the standard error for the data sets?

Answer 1

Given

n1 = 45

Mean , x̄1 = 111

Variance, s1²: 152.82

Standard Deviation, s1: 12.36

n2 = 30

Mean, x̄2 = 106.27

Variance, s2²: 204.823

Standard Deviation, s2: 14.312

Test statistic t =  (xbar1-xbar2)/sqrt(s1^2/n1+s2^2/n2)

= (111-106.27) / sqrt( 152.82 / 45 + 204.823 / 30)

= 1.479

P-value from t -score = 0.072

Pooled SD , Sp² = ( (n1-1)*s1² + (n2-1)*s2² ) /n1+n2-2 = (6724.08 + 5939.87) / 73

= 173.48

Standard error = Sp * sqrt( 1/n1 + 1/n2 )

= sqrt(173.48) * sqrt(1/45 + 1/30) = 3.10

95% C.I is

= (x1-x2) +/- t-critical * Estimated standard error

= (111-106.27) +/- 1.993 * 3.10

= 4.73 +/- 6.1783

= -1.45 , 10.9