Biologist Theodore Garland, Jr. studied the relationship between running speeds

Question

Biologist Theodore Garland, Jr. studied the relationship between running speeds and morphology of 49 species of cursorial mammals (mammals adapted to or specialized for running). One of the relationships he investigated was maximal sprint speed in kilometers per hour and the ratio of metatarsal-to-femur length. A least-squares regression on the data he collected produces the equation y = 37.67 + 33.18x where x is metatarsal-to-femur ratio and y is predicted maximal sprint speed in kilometers per hour. The standard error of the intercept is 5.69 and the standard error of the slope is 7.94. Construct a 90% confidence interval for the slope of the population regression line. Give your answers precise to at least two decimal places. Lower limit: Upper limit:

Explanation / Answer

here estimated slope b1 =33.18

std error of slope =7.94

at (n-2=47) degree of freedom and 90% confidence interval ; t=1.6779

hence 90% confidence interval =sample mean -/+ t*std error =19.8573 ; 46.5027

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