Question

5) A company that manufactures baseball bats believes that its new bat will allow players to hit the ball for 30 feet farther than its current model. The owner hires a professional baseball player known for hitting home runs to hit ten balls with each bat and he measures the distance each ball is hit to test the company’s claim. The results of the batting experiment are shown in the following table. Construct and interpret a 90% confidence interval for the true difference between the mean distance hit with the new model and the mean distance hit with the older model. Assume that the variances of the two populations are the same. Round your CI limits to 1 decimal place. HItting distance in feet

New model: 235 240 253 267 243 237 250 241 251 248

Old model : 200 210 231 218 210 209 210 229 234 231

Answer 1

x1    =	246.50	x2      =	218.200
s1    =	9.45	s2      =	12.072
n1    =	10	n2     =	10
Pooled Variance Sp2=((n1-1)s21+(n2-1)*s22)/(n1+n2-2)=				117.5611

Point estimate : x1-x2=			28.3000
standard error se =Sp*√(1/n1+1/n2)=			4.8489

for 90 % CI & 18 df value of t=			1.734
margin of error E=t*std error =			8.4081
lower bound=mean difference-E=			19.8919
Upper bound=mean differnce +E=			36.7081
from above 90% confidence interval for population mean =(19.9 , 36.7)