Question

A 1996 study identified 102 out of 852 men as left-handed vs 76 out of 839 women as left handed. The same study also looked at the difference in intelligence between right- and left-handed people. In particular, the average IQ of all right-handed persons in the sample (men and women) was x1 = 97.7, with a standard deviation of s1 = 15.4, whereas the average IQ of all left-handed persons in the sample (men and women) was x2 = 100.3, with a standard deviation of s1 = 17.6. (a) Set up a two-sided hypothesis test on a difference of means and determine the p-value for this sample data. (b) Can it be concluded that left-handed individuals are smarter than right-handed individuals given a significance level of α = 0.05? (c) What is the smallest significance level α (rounded to the nearest hundredth) for which we may conclude that lefties are smarter than righties?

Answer 1

Total number of people = 852 + 839 = 1691

Number of left handed people = 102 +76 = 178

Number of right handed people = 1691 - 178 = 1513

(a)

Since sample sizes are very large so we can use z test instead of t test.

Conclusion: There is no evidence to conclude that there is difference in intelligence between right- and left-handed people..

(b)

Here we need left handed test.

Conclusion: There is evidence to conclude that  left-handed individuals are smarter than right-handed individuals given a significance level of α = 0.05.

(c)

For , p-value remain smaller than level of significance. So at we may conclude that lefties are smarter than righties.