Based on a study of the circulation of 23 magazines, the audited newsstand sales
ID: 3173477 • Letter: B
Question
Based on a study of the circulation of 23 magazines, the audited newsstand sales are related to the reported sales by the prediction line Y_1 = 26.0492 + 0.5279X_1 (measured in thousands). For these data. S_YX = 43.445. X = 402 and, h_1 = 0.217 when X = 400. Complete parts (a) through (c). Construct a 95% confidence interval estimate of the mean audited sales for magazines that report newsstand sales of 400,000. lessthanorequalto muY|X = X_400 lessthanorequalto (Round to four decanal places as needed.) Construct a 95% prediction interval of the audited sales for an individual magazine that reports newsstand sales of 400,000. lessthanorequalto Y_400 lessthanorequalto (Round to four decanal places as needed.) Explain the differences in the results from (a) and (b). Since there is more variation in estimating a mean value than in predicting an individual value, the confidence interval is narrower than the prediction interval, holding everything else fixed. Since there is more variation in estimating a mean value than in predicting an individual value, the confidence interval is wider than the prediction interval, holding everything else fixed. Since there is more variation in predicting an individual value than in estimating a mean value, the prediction interval is wider than the confidence interval, holding everything else fixed. Since there is more variation in predicting an individual value than in estimating a mean value, the prediction interval is narrower than the confidence interval, holding everything else fixed.Explanation / Answer
Solution:
a)
Predicted value of Y for observation
b0 = 26.0492 and b1 = 0.5279
Yi = 26.0492 + 0.5279 (400) = 237.21
i = 26.0492 + 0.5279 (400) = 237.21
SYX = 43.445 and hi = 0.217
Y ± t/2SYX hi =
= 237.21± 2.3060(43.445) 0.217
= 237.21±100.180.217
= 237.21±100.18 (0.466) =
= 237.21± 46.68
190.53 YX = 400 283.89
b)
b0 = 26.0492 and b1 = 0.5279
Yi = 26.0492 + 0.5279 (400) = 237.21
i = 26.0492 + 0.5279 (400) = 237.21
SYX = 43.445 and hi = 0.217
Y± t/2SYX (1 + hi) =
=237.21± 2.3060(43.445 (1 + 0.217) =
=237.21 ± 100.18 (1.103)
=237.21 ± 110.49
126.72 YX = 400 347.7
=126.72 YX = 400 347.7
c) B. Since there is more variation in estimating a mean value than in predicting an individual value, the confidence interval is wider than the predition interval, holding everything else fixed.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.