A study was conducted to investigate the relationship between severe headaches and being left- or right-handed. (Incidentally, Lisa Kudrow, who played Phoebe Buffay on the hit sitcom "Friends," is an author on this study.) Of 273 participants with cluster headaches, 24 were left-handed. Of 477 participants with migraine headaches, 42 were left-handed.

(a) Give an estimate for the proportion of cluster headache sufferers who are left-handed.

(b) Use StatKey or other technology to construct and interpret a 95\% confidence interval for the proportion of cluster headache sufferers who are left-handed.

(c) Give an estimate for the proportion of migraine sufferers who are left-handed.

(d) Use StatKey or other technology to construct and interpret a 95\% confidence interval for the proportion of migraine sufferers who are lefthanded.

(e) Compare your confidence intervals in parts (b) and (d). Which is more narrow? Explain why.