Question

(15pts) A researcher wants to compare IQ scores for boys and girls. He obtained IQ scores for 47 randomly sampled seventh-grade boys in a Midwest school district and 31 seventh- grade girls in the same district.

1. (a) Based on the design, which test should the researcher use to analyze the data? One-sample t test, matched-pair t test or two-sample t test?(2pts)

2. (b) Based on the JMP output below, report the 95% CI for the mean IQ score difference between boys and girls. (5 pts)

3. (c) Use the 95% CI above to test whether the mean IQ score between boys and girls are significantly different or not, explain the reasoning(3pts).

4. (d) Based on the JMP output below, use the p-value method to test whether boys and girls differ in their mean IQ scores. State the null and alternative hypotheses, report the test statistic, p-value and your final conclusion. (5 pts)

JMP OUTPUT t Test

Male-Female
Difference 5.119

t Ratio 1.643877 DF 56.93171

5

  

Std Err Dif
Upper CL Dif
Lower CL Dif Confidence 0.95

3.114 11.354 -1.117

Prob > |t| Prob > t Prob < t

0.1057 0.0529 0.9471

Answer 1

Solution:

Given data:

a) Two -sample test.

b)

100(1- )% Confidence interval for difference of true means is :

95% confidence interval for the mean IQ score difference between boys and girls is:

=(-1.117,11.354)

Therefore 95% two sided confidence interval for the mean IQ score difference between boys and girls is -1.117 <   < 11.354.

c)

There is difference between the mean IQ score between boys and girls .since the confidence interval contains zero.

d)

Null hypothesis Ho:

Alternative hypothesis Ha:

Level of significance =0.05 then the critical values are -t(0.025,47+31-2)=-2and t(0.025,76)=2,it falls in acceptance region ,we fail to reject the null hypothesis

p-value =2p(t > 1.6438)

=0.1043

p-value greater than the level of significance =0.05.

So we fail to reject the null hypothesis.