A neurological study found that monozygotic twins share numerous physical, psychological, and pathological traits. The researchers measured intelligence scores of 10 pairs of twins. The twins are distinguished by birth order. Assume Normality.

a) Show all steps (including how to find cutoff value) and construct a two-sided 95% Confidence Interval for the true mean difference.

(b) Figure out to the nearest whole percent what confidence level you would need to decrease to obtain a confidence width (error) of about 0.22 for the true mean difference in this prob

BornFirst BornSecond
6.08 5.73
6.22 5.8
7.99 8.42
7.44 6.48
6.48 6.43
7.99 8.76
6.32 6.32
7.6 7.62
6.03 6.59
7.52 7.67