$16\mathrm{.}139$ Xr$16-139*$ A computer dating service typically

asks for various pieces of information such as

height, weight, income, and so on$.$ One such service

requested the length of index fingers. The

only plausible reason for this request is to act as

a proxy on height. Women have often complained

that men lie about their heights. If there is a strong

relationship between heights and index fingers, the

information can be used to $$correct$$ false claims

about heights. To test the relationship between the

two variables researchers gathered the heights and

lengths of index fingers print $($in millimeters$)$ of $200$

students $($males and females$).[$use only the male data$]$

a$.$ Graph the relationship between the two

variables.

b$.$ Is there sufficient evidence to infer that

height and length of index fingers prints are linearly

related?

c$.$ Predict with $95\%$ confidence the height of

someone whose index finger print is $26$ mm long. Is

this prediction likely to be useful? Explain.