1. The data set in this question consists of IQ scores of 7th grade boys and gir

Question

1. The data set in this question consists of IQ scores of 7th grade boys and girls from a Midwestern school district. Use Excel to answer the following questions. Boys Girls 107 100 00 104 107 89 115 102 11191 97114 112 114 104 103 106 105 113 108 10 130 113120 132 128111 118 128 124 127 124 a. Are the data from matched pairs design? b. What are the means for the two groups? c. What is the two standard deviations for the two groups? d. We want to see if there is a significant difference between the two groups. State your null and alternative hypothesis. e. Calculate the test statistics (Assuming unequal variances): f. What is the two-sided p-value for comparing the means of the two groups? Give your decision. g. What conclusion do you reach? State in words a non-statistician would understand h. Use Excel to get the output of data analysis "t-Test: Two-Sample assuming unequal variances", and print it. I. What is the two sided t critical value in the table in 1? Make 95% C1. Can you get the same conclusion (based on 95% CI ) as that in g?

Explanation / Answer

Excel output :

a) No the data is not from matched pairs design

b)

Mean IQ of boys 114.96

Mean IQ of girls 110.0666667

c)

SD of IQ of boys 9.850888285

SD of IQ of girls 13.15004979

d)

H0: mu1 - mu2 = 0

H1: mu1 - mu2 not equals to 0

e)

Test statistics, t = 1.246538049

f)

p-value = 0.225113543

g)

Fail to reject the null hypothesis

t-Test: Two-Sample Assuming Unequal Variances Boys Girls Mean 114.96 110.0666667 Variance 97.04 172.9238095 Observations 25 15 Hypothesized Mean Difference 0 df 23 t Stat 1.246538049 P(T<=t) one-tail 0.112556772 t Critical one-tail 1.713871528 P(T<=t) two-tail 0.225113543 t Critical two-tail 2.06865761

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