Consider the following random sample of diameter measurements (in inches) of 19 softballs.

Question

Consider the following random sample of diameter measurements (in inches) of 19 softballs.

4.83, 4.77, 4.84, 4.76, 4.83, 4.79, 4.88, 4.72, 4.72, 4.76, 4.73, 4.89, 4.7, 4.75, 4.81, 4.75, 4.75, 4.79, 4.9

If we assume that the diameter measurements are normally distributed, find a 95% confidence interval for the mean diameter of a softball. Give the lower limit and upper limit of the 95% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places.

Answer 1

calculate the mean = arithmetic average

= sum of the 19 numbers divided by 19

= 4.8 -24/19 = 331/95

=(4.83+4.77+4.84+4.76+4.83+4.79+4.88+4.72+4.72+4.76+4.73+4.89+.47+4.75+4.81+4.75+4.75+4.79+4.9)/19

= 4 +1497/1900= about 4.787

calculate standard deviation= sqrVar= 0.060

Var=Variance = sum of squared deviations from the mean= sum of (each x-mean)^2

calculate z score

use n=19

CI = Confidence Interval = (mean+/- z score)

= (4.76. 4.82)