********************************************************* PClab #4 There are 2 pop machines. One is a regular pop machine and it costs 75 cents for a pop. The other is a RANDOM POP MACHINE painted in flashy colors and it plays wild, enticing music to attract attention. The random pop machine has 2 buttons on its front marked "toss 2 coins - 2 heads gets you a free pop". When the 1st button is punched the result of the toss is shown on a screen - heads or tails. The 2nd button does the same. The chance of heads is 1/2 for each button. You put $1 in the random pop machine to play. You punch the two buttons and if you get 2 heads your $1 is returned with your pop. Otherwise, you get your pop, but it keeps your $1. (A moments thought shows that you get a free pop with chance 25% and a pop costs you $1 with chance 75%.) (1) Use Minitab to simulate 500 attempts at the random pop machine (about a semesters' worth of pop?). Use the session window commands: MTB> random 500 C1 ; # note this line ends in a semicolon SUBC> binomial 1 .75 . # note this line ends in a period The resulting column C1 contains the costs (random) for 500 purchases. To get the sum of this column, the total amount spent, use the command: MTB> sum C1 Repeat this 5 times and record your sums. (2) Use our theory concerning random draws to figure out the expected value and standard deviation for the sum of 500 such "draws". How did your 5 results in part (1) match the theory? (3) The following data gives the warp breakage during the weaving of fabric for a sample of yarns. 86 146 251 653 98 249 400 292 131 169 175 176 76 264 15 364 195 262 88 264 157 220 42 321 180 198 38 20 61 121 282 224 149 180 325 250 196 90 229 166 38 337 65 151 341 40 40 135 597 246 211 180 93 315 353 571 124 279 81 186 497 182 423 185 229 400 338 290 398 71 246 185 188 568 55 55 61 244 20 284 393 396 203 829 239 236 286 194 277 143 198 264 105 203 124 137 135 350 193 188 Copy the data and paste it into the MINITAB spreadsheet in C1 to C10. To arrange these values into one column use the session command: Stack c1-c10 c11 Name column C11 "breakage". Give a dotplot of the data. Give a histogram of the data. Further, try to experiment with the choice of intervals by using the session command like: MTB> histogram C1 ; SUBC> cutpoints 0 50 100 150 500 . Choose your own values for the cutpoints - they specify the boundaries of the intervals you want to use. Produce a dotplot for the data. Get descriptive statistics for breakage. By hand, calculate a 95% confidence interval for the proportion of times the breakage exceeds 300 . (Count how many times this happens.) By hand, or with Minitab, calculate a 95% confidence interval for the mean breakage of the underlying population.