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

The 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 is between 21.6 and 35.0.

We are 90% confident that the true difference between the mean distance hit with the new model and the mean distance hit with the older model is between 21.6 and 35.0.

New	Old	Difference
235	200	35
240	210	30
253	231	22
267	218	49
243	210	33
237	209	28
250	210	40
241	229	12
251	234	17
248	231	17
	246.500	mean New
	218.200	mean Old
	28.300	mean difference (New - Old)
	11.528	std. dev.
	3.646	std. error
	10	n
	9	df
	21.6	confidence interval 90.% lower
	35.0	confidence interval 90.% upper
	6.683	margin of error