4-5 Simulations for Hypothesis Tests 193 randomly generated, then the samples are analyzed to determine whether three or more birthdays are the same. Instead of using actual birthdays, we can use the integers 1, 2, 3, . . . , 365, where 1 = January 1, 2 = January 2, . . . , 365 = December 31. A computer can be used to generate such samples of 100 simulated birthdays. (Most statistics software packages provide a feature for generating random integers.) Here is one sample, with the simulated birthdays sorted so that it becomes easy to see whether three or more are the same: 4 7 7 9101114151618 21 25 34 36 37 45 46 61 65 70 75 79 87 92 97 101 105 107 109 110 113 113 113 114 116 123 130 139 142 142 148 149 157 162 173 173 174 174 181 183 185 186 192 192 192 197 201 203 206 211 215 215 225 234 234 235 237 238 240 241 243 245 247 247 252 265 269 270 272 272 273 273 304 315 318 320 321 321 323 327 332 333 337 340 340 357 358 361 363 364 Because the birthdays have been sorted, it is easy to scan through the above sample to see that there are three (or more) simulated birthdays that are the same. (For this sample, there are two birthdays that occur three times: 113 and 192). We could now continue to generate more samples and, in each case, determine whether three or more birthdays are the same. We can repeat as often as needed to get a good estimate of the probability that among 100 randomly selected people, at least three share the same birthday. YOUR TURN. Do Exercise 13 “Simulating the Monty Hall Problem.” Generating Simulated Data Access tech supplements, videos, and data sets at www.TriolaStats.com TECH CENTER Statdisk 1. Click Data in the top menu. 2. Select the desired type of data generator from the dropdown menu. Options include: • Normal Generator • Uniform Generator • Binomial Generator 3. Enter the required inputs (varies depending on the type of generator selected). 4. Click Generate. StatCrunch 1. Click Data in the top menu. 2. Select Simulate in the dropdown menu. 3. Select the desired type of data generator from the dropdown menu. Options include: • Normal • Uniform • Binomial 4. Enter the required inputs (varies depending on the type of generator selected). 5. Click Compute. Minitab 1. Click Calc in the top menu. 2. Select Random Data from the dropdown menu. 3. Select the desired type of data generator from the dropdown menu. Options include: • Normal • Uniform • Integer (uniform distribution) • Binomial 4. Enter the required inputs (varies depending on the type of generator selected). 5. Click OK. continued
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