Carleton University - School of Mathematics and Statistics STAT 2601 - Fall 2022 - Assignment #3 Due on Wednesday, November 2 before 9am Instructions: Please refer to the document entitled Assignment Submission Regulations posted on I Brightspace. Follow the instructions carefully. QUESTION 1. Billy's Fizzy Flavours Inc. has introduced a new soft drink called Crazy 88 Cola. They wish to estimate the proportion of consumers who would buy the soft drink. (a) They want their estimate to be accurate to within 8.8 percentage points with 99% confidence. How many consumers should they randomly select to accomplish this goal? (b) A random sample of 500 consumers tasted the new soft drink, and 185 of them said they would buy it. Compute and interpret a 95% confidence interval for the proportion of all consumers who would buy Crazy 88 Cola. (c) Do you think the result in part (b) is valid? Explain. QUESTION 2. Billy's Fizzy Flavours Inc. wants to estimate the average volume per can of Crazy 88 Cola with 90% confidence. (a) In practice, the soft drink producer does not know the population mean or population standard deviation of the volume per can. However, for the purpose of this question we will assume the volume per can is normally distributed with a mean of 353 mL and a standard deviation of 2 mL. Use this information and the MacBook Air esc 388 FIO @ A W . N 4 8 Q W E R Y U O 11 A S D F G H J K . . . . Z X ? C V B N M option command MOSISO command optionCO A brightspace.carleton.ca C TutorOcean | Co.. sign out Untitled docume. sign In INP WileyPLUS Mi transfer - ethan . Business Memo . Del Assignment #3 -. https:/br (a) In practice, the soft drink producer does not know the population mean or population standard deviation of the volume per can. However, for the purpose of this question we will assume the volume per can is normally distributed with a mean of 353 mL and a standard deviation of 2 mL. Use this information and the Excel procedure demonstrated in Lab #3 to generate 50 independent random samples of size n = 6 cans from the production line, and compute the confidence intervals for the population mean using a 90% confidence level. In computing the confidence intervals, assume that you do not know the population standard deviation. Note: The complete spreadsheet must be included as part of your PDF file submission. Use the landscape orientation, not the default portrait orientation, to ensure all columns appear on each page. (b) Prior to generating the random samples, how many of the 50 confidence intervals in part (a) did you expect to contain the population mean of 353 mL? Explain. (c) According to your output in part (a), how many of the 50 confidence intervals successfully captured the population mean of 353 mL? Will this always match the value in part (b)? Explain. (d) Write down the six (6) observations you obtained for Sample #1 (rounded to two decimal places). Use these observations to show how, by hand, how the first confidence interval was computed. Interpret the result. (e) When we compute confidence intervals using the z-based formula, the length of every interval is the same. However, when we compute confidence intervals using the t-based formula, the length of every interval is different. Why? QUESTION 3. My barber claims that, on average, it takes him less than 20 minutes to give someone a haircut. A random sample of 9 haircuts yielded a mean of 17.25 minutes. Assume haircut times are normally distributed with a population standard deviation of 3.5 minutes. Is there sufficient evidence to support my barber's claim? To answer this question, conduct a hypothesis test using the p-value method at the 5% significance level. MacBook Air esc #: % W. N 5 Q W E R U O P A S D F G H J K . . . . ? Z X C V B N M 96 option command MOSISO command option8+ 76907 brightspace.carleton.ca Sign out Untitled docume.. Sign In WP WileyPLUS Business Memo.. DZL. STAT 2601 Lab 3... B https://brig 1 of 2 - + Automatic Zoom v Sample # sample mean sample st dev LB UB SUCCESS 1 68.966 56.302 48.029 69.129 52.939 60.871 61.889 58.403 53.965 52.77 58.32624007 6.977188366 53.3351 63.3174 2 81.891 77.018 39.107 81.144 47.899 72.028 40.095 75.536 64.184 75.368 65.42702446 16.80031765 53.4088 77.4452 3 48.017 56.718 65.657 53.183 51.908 80.964 66.889 49.21 73.565 46.344 59.24537497 11.86266643 50.7593 67.7314 4 48.239 73.586 44.614 58.906 57.201 57.39 61.374 50.064 41.25 61.022 55.36446512 9.509181611 48.562 62.1669 575.084 51.084 47.251 64.494 76.998 65.451 56.871 63.397 55.214 81.532 63.73757575 11.43390277 55.5583 71.9169 6 53.83 51.336 59.102 60.69 40.232 38.755 88.876 89.968 38.825 54.971 57.65858001 18.58103588 44.3665 70.9507 74.277 49.517 46.278 48.164 68.75 63.324 51.281 38.933 65.811 67.962 57.42974614 11.92875969 48.8964 65.9631 8 59.808 49.189 65.07 38.545 62.605 45.399 84.037 65.062 57.552 50.967 57.82329724 12.76496009 48.6918 66.9548 9 61.159 38.843 70.69 56.588 53.412 51.305 55.121 35.804 38.618 46.742 50.82812565 11.02983888 42.9379 58.7184 10 86.847 68.824 62.612 63.198 68.748 51.304 64.504 58.444 87.1 72.496 68.40760686 11.4222122 60.2366 76.5786 11 55.588 58.017 53.123 56.807 73.334 49.128 43.742 49.067 73.712 49.004 56.15230263 10.11927104 48.9134 63.3912 12 66.651 59.17 60.508 66.799 64.871 46.715 61.392 30.636 55.899 41.546 55.41880015 12.03381064 46.8103 64.0273 3 47.928 54.392 98.641 57.518 57.316 54.605 58.896 50.055 64.34 60.627 60.43180171 14.26040631 50.2305 70.6331 14 53.798 49.997 67.955 79.905 63.877 71.091 69.729 40.968 67.242 73.608 63.81695691 11.94846024 55.2695 72.3644 5 70.365 74.386 61.183 69.883 49.876 59.479 63.307 57.125 65.899 67.296 63.87999444 7.248952827 58.6944 69.0656 6 66.688 64.349 47.731 56.78 69.797 56.363 54.424 66.961 56.171 72.018 61.12848738 7.8854615 55.4876 66.7694 7 65.833 52.716 43.981 63.134 62.272 56.574 60.105 69.113 68.277 80.44 62.24441146 9.94106523 55.133 69.3558 8 73.077 55.614 60.102 72.173 80.499 53.465 61.103 67.801 67.008 53.349 64.4191197 9.198392832 57.839 70.9993 19 66.433 65.992 68.006 75.318 72.912 45.096 55.926 76.064 70.462 61.583 65.77917081 9.530604674 58.9614 72.597 20 58.264 62.313 68.034 40.661 61.434 66.981 44.21 51.5 65.435 50.887 56.97190515 9.661791917 50.0603 63.8835 21 45.04 43.443 46.656 82.353 50.905 60.994 69.774 67.1 60.303 70.01 59.65767756 12.92884971 50.4089 68.9064 22 54.662 37.72 45.261 62.887 63.881 63.984 46.971 45.62 26.549 57.355 50.48903237 12.3796377 41.6332 59.3449 23 75.235 26.681 56.581 59.763 71.176 46.119 47.471 56.164 43.603 57.245 54.00392289 13.98477801 43.9998 64.008 24 65.698 69.614 50.967 61.52 58.828 49.565 68.437 71.378 64.956 59.91 62.0874445 7.458773992 56.7518 67.4231 25 46.635 73.022 40.088 37.756 80.164 61.377 53.067 53.211 74.62 85.088 60.50269591 16.94018225 48.3844 72.621 26 52.326 58.642 47.336 64.697 66.79 54.695 78.888 64.518 64.628 61.411 61.3929839 8.810455033 55.0904 67.6956 27 73.191 50.158 72.466 68.082 60.745 56.058 40.084 65.306 57.856 34.436 57.83816611 13.09725034 48.469 67.2074 28 80.179 65.741 58.454 40.15 69.229 72.297 70.755 40.821 57.775 83.305 63.87055934 14.73740752 53.3281 74.4131 29 38.239 48.789 86.344 68.365 64.262 59.681 66.503 59.532 48.194 66.058 60.59687636 13.31890723 51.0691 70.1246 30 44.023 56.052 52.784 55.212 53.125 39.429 58.364 59.051 56.302 50.046 52.43891489 6.332389236 47.909 56.9688 31 43.715 69.635 72.323 31.206 61.013 56.511 66.25 49.502 70.291 39.165 55.96121052 14.44652138 45.6268 66.2956 32 61.703 58.748 61.098 42.362 53.738 49.749 91.557 76.019 57.853 32.421 58.524695 16.52274008 46.705 70.3444 33 62.307 51.516 69.763 46.971 65.988 79.423 73.353 52.326 58.878 65.296 62.58209548 10.30271279 55.212 69.9522 34 50.627 67.923 45.771 51.663 53.664 72.507 59.822 70.127 52.565 77.899 60.25683357 11.03903179 52.36 68.1537 MacBook Air 80 988 F3 FA DD F7 F8 F9 @ # o 3