Question

16 A- According to the 2017 Corporate Travel Index compiled by Business Travel News, the average daily cost for business travel in the United States rose to $321 per day (Executive Travel website). The file Travel contains sample data for an analogous study on the estimated daily living costs for an executive traveling to various international cities. The estimates include a single room at a four-star hotel, beverages, breakfast, taxi fares, and incidental costs. Click on the datafile logo to reference the data. DATA file City Mexico City Milan Mumbai Paris City Bangkok Bogota Cairo Dublin Frankfurt Hong Kong Johannesburg Lima London Madrid Daily Living Cost ($) 242.87 260.93 194.19 260.76 355.36 346.32 165.37 250.08 326.76 283.56 Rio de Janeiro Seoul Tel Aviv Toronto Warsaw Washington, D.C. Daily Living Cost ($) 212.00 284.08 139.16 436.72 240.87 310.41 223.73 181.25 238.20 250.61 a. Compute the sample mean (to 2 decimals). b. Compute the sample standard deviation (to 2 decimals). c. Compute a 95% confidence interval for the population standard deviation (to 2 decimals). Use Table 11.1. 95%CI= A

Answer 1

Solution: X dx = x - Α = Χ - 260 dx2 242.87 -17.13 293.4369 260.93 0.93 0.8649 194.19 -65.81 4330.9561 260.76 0.76 0.5776 355.36 95.36 9093.5296 346.32 86.32 7451.1424 165.37 -94.63 8954.8369 250.08 -9.92 98.4064 326.76 66.76 4456.8976 283.56 23.56 555.0736 212 -48 2304 284.08 24.08 579.8464 139.16 -120.84 14602.3056 436.72 176.72 31229.9584 240.87 -19.13 365.9569 310.41 50.41 2541.1681 223.73 -36.27 1315.5129 181.25 -78.75 6201.5625 238.2 -21.8 475.24 250.61 -9.39 88.1721 Σx = 5203.23 Σ (dx) = 3.23 Σ (dx)2 = 94939.4449
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ΣΧ Mean X = n 242.87 +260.93 + 194.19 +260.76 + 355.36 + 346.32 + 165.37 + 250.08 + 326.76 + 283.56 +212 +284.08 + 139.16 + 436.72 + 240.87 + 310.41 + 223.73 + 181.25 +238.2 + 250.61 20 5203.23 20 = 260.1615 X = 260.1615 is not an integer, use assumed mean method A = 260

Sample Standard deviation S = 1 (Σdx) 2 Σdx2. n η - 1 94939.4449 - (3.23)2 20 = 19 194939.4449 - 0.5216 19 Π 194938.9233 19 = V4996.7854 = 70.6879

Solution: The provided sample mean is Ž = 260.16 and the sample standard deviation is s 70.69. The size of the sample is n = 20 and the required confidence level is 95%. The number of degrees of freedom are df = 20 – 1= 19, and the significance level is a = 0.05. Based on the provided information, the critical t-value for a : 0.05 and df = 19 degrees of freedom is to = 2.093. The 95% confidence for the population mean u is computed using the following expression C1 = ( x - * * * )

Therefore, based on the information provided, the 95 % confidence for the population mean u is 2.093 x 70.69 CI = ( 260.16 – V20 260.16 + (260.16 – 33.084, 260.16 + 33.084) (227.076, 293.244) which completes the calculation.