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Question 1 A sample of n=16 observations is drawn from a normal population with $1000 and 63200. Find the following: a) (10 points) P0? 2: 1070) b) (15 points) P(990 q 2 s 1150} Question 2 (25 points) In an attempt to assess total daily travel taxes in various cities, the Global Business Travel Association conducted a study of daily travel taxes on lodging, rental car, and meals. The data Contained in the file TravelTax.xls are consistent with the findings of that study for business travel to Chicago. Assume the population standard deviation is known to be $3.50 and develop a 95% confidence interval of the population mean total daily travel taxes for Chicago. Question 3 (15 points) Determine the probability that in a sample of 100 the sample proportion is less than 0.77 if p=0.8. Question 4 U.S. National Bureau of Standards defines ' ' specification" as follows: A set of conditions and requirements, of specific and limited application, that provide a detailed description of the procedure, process, material, product, or service for use primarily in procurement and manufacturing. OPRE 6301- Statistics and Data Analysis Homework 3 A nonconformity is a quality characteristic that does not meet stipulated specifications. A nonconforming unit has one or more nonconformities such that the unit is unable to meet standards (or specifications) and is unable to function as required. For example, the specifications for the inside diameter of an axle might be 2:0.1 centimeters. This means that an axle with an inside diameter of 2.2 centimeters (or 1.8 centimeters) is defective. A company has been working to decrease the proportion of defective items among those delivered to one of its major buyers. The specifications set by this purchaser for a certain quality characteristic are within 20.0:03 units. The following measurements have been reported for a sample of 50 items: 20.10 19.75 20.20 20.15 19. 90 20.00 19.65 19.92 19.80 20.13 19.98 20.05 20.20 20.23 20.31 20.01 20.49 19.99 20.13 20.18 20.03 19.87 19.93 20.11 20.2 2 19.84 20.12 20.24 20.03 20.08 20.00 20.11 20.99 20.33 20.11 19.89 20.32 19.76 20.05 19.97 20.05 19.85 19.87 19.67 20.06 19.95 20.09 20.10 19.90 19.73 a) (10 points) Find a 90% confidence interval for the proportion of nonconforming items. Comment on your result. 1)) (10 points) Find a 95% confidence interval for the proportion of nonconforming items. Discuss and interpret the differences of the two confidence intervals (in Parts (a) and (b)). c) (15 points) Can we conclude that the percent nonconforming of all items delivered to the current buyer is more than 13%? Use a level of significance 0.05. AutoSave O OFF MAGIC ... hw 3TravelTax (1) Home Insert Draw Page Layout Formulas Data Review View ? Tell me & Cut Times New Roman v 12 A A ab Wrap Text General Copy Paste Format B Uv MvAv Merge & Center $ ~ % 9 00 -20 Conditional Format Formatting as Table A1 X fx Lodging, Car Rental, and Meal Taxes ($) H J K L M N P Q R S Lodging, Car Rental, and Meal Taxes ($) 38.02 41.89 47.44 40.14 47.69 44.02 32.93 33.32 33.90 36.53 43.01 33.22 35.65 39.47 38.86 42.42 47.71 45.03 53.73 36.07 49.95 31.81 63.43 31.50 64 .13 42.14 46.78 30.45 47.35 39.42 39.79 43.63 34.03 35.74 48.43 30.92 44.45 41.63 27.23 41.03 43.87 46.07 34.34 39.57 36.40 48.18 42.92 35.57 45.68 43.14 52 55.21AutoSave OFF A A FDC ... ahw 3TravelTax (1) Home Insert Draw Page Layout Formulas Data Review View Tell me Times New Roman v 12 AA E = 7 V ab Wrap Text General [E Copy Paste Conditional Form Format BI UV MvAv Merge & Center v $ % Formatting as Tabl A1 X fx Lodging, Car Rental, and Meal Taxes ($) H K L M N P Q R 42.92 35.57 45.68 43.14 55.21 34.73 26.40 40.66 37.66 28 .63 8.17 45.16 46.19 49.58 48.14 45.61 34.22 44.34 55.14 37.00 48.78 52.77 49.07 45.35 2.59 41.27 20.93 30.70 43.00 38.56 41.31 39 .18 33.57 25.09 30.05 19.28 32.47 53.97 47.32 35.61 44.11 38.97 37.48 40.55 52.03 46.86 46.07 34.89 42.93 49.64 100 44.35 101 41.66hw 3TravelTax (1)~ AutoSave O OFF Home Insert Draw Page Layout Formulas Data Review View ? Tell me & Cut Times New Roman v 12 AA = 27 V ab Wrap Text Genera CE Copy v Conditional Format Paste B I MVAv = Merge & Center v $ ~ % " Formatting as Table Format A1 X fx Lodging, Car Rental, and Meal Taxes ($) L M N 0 P Q R S A 99 49.64 100 44.35 101 41.66 102 39.80 103 50.31 104 36.59 105 33 .40 106 45.51 107 44.43 108 47.65 109 36.24 110 32.03 32.81 31.64 40.18 34.13 33.22 48.60 40.66 43.37 41.08 120 34.11 121 52.91 122 $1.76 123 56.03 124 33 .61 125 10.11 126 53.77 127 34.73 128 35.58 129 18.28 130 31.89 131 34.71 132 37.44 34.77 134 31.82 135 39.98 136 44.66 137 31.78 138 21.69 139 43.23 140 54.00 141 46.55 142 44.85 143 42.15 144 25.67 145 50.25 146 44.62 147 44.30 148 45.09 149 35 .12 150 $4.06 151 31.773hw 3TravelTax (1) AutoSave OFF A A FDC ... Home Insert Draw Page Layout Formulas Data Review View Tell me Times New Roman v 12 AA E 2 7 V ab Wrap Text General [ Copy Conditional Forma paste BI UV MVAv SE Merge & Center v $ ~ % 9 Formatting as Table Format A1 + X V fx Lodging, Car Rental, and Meal Taxes ($) H K M N P Q R 149 35.12 150 $4.06 151 31.77 152 36.55 153 36.79 154 29.65 155 47.66 156 25.91 157 47.27 158 32.31 159 42.52 160 46.86 161 48.75 162 38.81 163 33.66 164 27.24 165 46.40 166 50.95 167 39.74 168 35.47 169 35.95 170 29.51 171 62.77 172 37.72 173 174 39.91 175 33 .28 176 39.63 177 28.57 178 38.14 179 36.04 180 40.13 181 35.51 182 31.49 183 39.49 184 37.69 50.34 186 44.10 187 45.61 188 46.51 189 53.00 190 35.40 191 25.64 192 47.65 193 47.49 194 195 45.41 196 28.77 197 37 .32 198 28 .64 199 50.67 200 33.77 201 40.88