Question

DATAfile: HongkongMeals You may need to use the appropriate appendix table or technology to answer this question. The mean cost of a meal for two in a midrange restaurant in City A is $47. How do prices for comparable meals in Hong Kong compare? The file HongkongMeals contains the costs for a sample of 42 recent meals for two in Hong Kong midrange restaurants. 22.78 36.88 26.32 33.89 38.55 19.57 22.77 41.68 36.57 28.79 31.89 33.51 18.04 | 23.29 | 35.28 | 42.38 25.73 34.19 | 31.75 25.24 32.97 36.83 30.1737.29 32.83 43.00 35.23 34.76 38.47 39.42 40.72 43.92 29.17 30.54 26.74 37.93 25.37 24.71 27.73 33.06 36.51 45.25 (a) With 95% confidence, what is the margin of error for the estimated mean cost in dollars for a mid-range meal for two in Hong Kong? (Round your answer to the nearest cent.) (b) What is the 95% confidence interval estimate of the population mean cost in dollars for a mid-range meal for two in Hong Kong? (Round your answers to the nearest cent.) to $ (c) How do prices for meals for two in mid-range restaurants in Hong Kong compare to prices for comparable meals in City A restaurants? The mean cost for a mid-range meal for two in City A is higher than the upper limit of the 95% confidence interval for comparable meals in Hong Kong. This suggests mean cost of comparable meals in Hong Kong is less than in City A.

Answer 1

Pazo NO Date: Solution - To consleuct 95°C, contidence Sotees margin of eelne Sample size (0)2 42 Here c=95%, x=0.05,2/2=0.025 The sample size (n) >30, so we use z table Zx12= 20.025 = 1.96 Noco x = Exi - 1371.78 = 32.66 n 42 s-Erai-x)2 - 1915.4429 n-1 V = 6:835) 41 a maegin of eceoe E = Zx12 s = 1.96 (6.8351) V42 = 2.067 Maegin of eceoe for the estimated mean cost in dollares for a mid- fange meal for two in Hong kong is $2.067 b) vn gr% confidence Inteeval is (n IZS) i el X - Zal , x + 204 ) (32-66-196 (6-8351), 32-667196 (6.8351) 142 142 (32.66-2.067, 32.66+2.067) (30.593, 34.727)

..95% confidence inte eval estimate of popwation mean cost Pn dollaes foɛ a mid-tange meal foe two in Hong kong is $30.593 to $34.727 The mean cost for mid-eange meal for two in City A is bighet than the uppea limit of the 95% confidence inte eval foe compacable meals in Hong Kong. This suggests mean cost of comparable meals in Hong kong is less than in city A.