Question

The value of a sports franchise is directly related to the amount of revenue a franchise can generate. The accompanying data table shows the annual revenue​ (in millions of​ dollars) and value​ (in millions of​ dollars) for 30 baseball franchises. Complete parts​ (a) through​ (c) below.

Revenue	Value
218	517
168	375
266	870
192	469
166	389
184	374
158	343
162	406
441	1602
160	295
194	436
157	319
177	454
166	322
171	374
190	449
248	723
166	329
186	381
146	314
189	450
249	727
166	350
269	862
229	539
140	294
200	491
162	403
199	483
184	389

a. Construct a 95​% confidence interval estimate of the mean value of all baseball franchises that generate ​$150 million of annual revenue.

b. Construct a 95​% prediction interval of the value of an individual baseball franchise that generates $150 million of annual revenue.

c. Explain the difference in the results of​ (a) and (b).Choose the best explanation below.

A. The prediction interval is wider than the confidence interval because simple linear regression is inadequate for analyzing these data. They should be the same.

B. The prediction interval is wider than the confidence interval because the standard deviation of the value data is larger than the standard deviation of the revenue data.

C. The prediction interval is wider than the confidence interval because there is more variation in predicting an individual value than in estimating a mean value.

D. The prediction interval is wider than the confidence interval because the franchise value data are larger than the franchise revenue data.

Answer 1

c.

Option C. The prediction interval is wider than the confidence interval because there is more variation in predicting an individual value than in estimating a mean value.