9. Chatterjee et al (1995. p 132) described two studies about the effect of condoms in reduc- ing the spread of AIDS. One two-year Italian study followed heterosexual couples where one partner was infected with the HIV virus. Of 171 couples who always used condoms, 3 partners became infected with HIV, while of 55 couples who did not always use con- doins, 8 partners became infected.

a) Estimate the infection rates for the two groups, and construct a 95% confidence inter- val to compare them. Interpret.

b) Test whether the rates are significantly different Report the P-value and interpret.