Question

The recommendations of respected wine critics have a substantial effect on the price of wine. Vintages that earn higher ratings command higher prices and spark surges in demand. These data are a random sample of ratings of wines selected from an online web site from the 2000 and 2001 vintages. Complete parts (a) through (d). Click the icon to view the table of wine rating, price, and vintage. (a) Do the ratings meet the conditions needed for a two-sample confidence interval? i Wine rating, price and vintage table. A. Yes, all the conditions are satisfied. OB. No, the 2000 data contains outliers, OC. No, the variances are drastically different. OD. No, the 2001 data is too skewed. O E. No, the sampling procedure was not identified and it cannot be concluded that this is a simple random survey Rating Rating (b) Find the 95% confidence interval for the difference in average ratings in these two vintages. Docs one of the years look better than the other? 88 .. The 95% confidence interval for zcoo - H2001 is (Round to one decimal place as needed.) Price Vintage 130 2000 30 2000 45 2001 9 2000 33 2001 117 2000 125 2001 19 2001 17 2000 33 2000 15 2001 36 2000 85 2001 Full data set o Price Vintage 72 2000 23 2001 40 2000 45 2000 50 2000 50 2000 29 2001 40 2000 42 2001 50 2001 50 2001 80 2000 23 2001 Print Done

Answer 1

The objective is to compute the 95% confidence interval for the difference in average ratings in these two vintages. The mean and standard deviation for the vintage 2000 is computed as follows: n 92 +93 +88+---+91+92 2(x, – F)? V -1 (92–91.6428)? +...+(92–91.6428)? 14 13 1283 14 =91.6428 = 13.4780 = 1.86 The mean and standard deviation for the vintage 2001 is computed as follows: S, = 12 V (x, - F, ) n2-1 (90-91.25)* +---+(91–91.25)? 90+91 +94 +---+93 +91 12 = = 1095 12 = 91.25 = V2.0227 =1.42 The pooled standard deviation is computed as follows:

(1, -1)x +(1, -1) sở PV +1, -2 (14–1)(1.86)²+(12-1)(1.42)? 14+12-2 = 72.811 =1.677 Degrees of freedom: df = n, +n, -2 = 14 +12-2 = 24 The critical value oft at 0.05 level of significance with 24 degrees of freedom is 2.0639. Hence, the 95% confidence interval for the difference in average ratings in these two vintages is computed as follows: CI = ( x - x)+10 S - +- n n =(91.6428 – 91.25)+ 2.0639 1.677/ha =(0.3928) +2.0639(0.6597) =(-0.968,1.754) =(-1.0,1.8) (Rounded to onedecimal place] Therefore, the 95% confidence interval for difference in average ratings in these two vintages is (-1.0, 1.8).