Fall Hint: criterion? d) Based measure of spread? Solution. Page 1
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1 Question #1 (12 Marks) The following are the golf scores of 12 members of a women s golf team in tournament play: Hint: n 1 x 2 i x a) Present the distribution by a stemplot and describe its main features. b) Compute the mean, variance, and standard deviation of these golf scores. c) Then compute the median, the quartiles, and the IQR. Are there any suspected outliers by the 1.5 IQR criterion? d) Based on the shape of the distribution, would you report the standard deviation or the quartiles as a measure of spread? Page 1
2 Question #2 (12 Marks) Battery packs in electric go-carts need to be able to last a fairly long time. The run-times (time until it needs to be recharged) of the battery packs made by a particular company are Normally distributed with a mean of 2 hours and a standard deviation of 20 minutes. a) What percentage of these battery packs lasts longer than 3 hours? b) Battery packs that have a run-time in the highest 10% of the run-time distribution are highly sought after by go-cart drivers. How long does the battery pack have to last for it to fall in this highly sought-after class? a) 0.13% b) 2 hours and 25.6 minutes Page 2
3 Question #3 (12 Marks) Simple random samples of 100 high school students are sampled from each grade level, for a total of 400 high school students. They are asked to rate the performance of the President of the United States on a scale from 1 to 5 (1 = poor, 5 = excellent). The results are presented below: a) What proportion of the studentss in the sample assigned the President an excellent rating? b) What proportion of the seniors in the sample assigned thee President an excellent rating? c) The data are goingg to be summarized by computing the conditional distributions of performance rating for students in each of the four classes. What would be the entry for freshmen who gave the President a poor rating? a) 32/400 = 0.08 b) 12/100 = 0.12 c) 20/100 = 0.20 Page 3
4 Question #4 (12 Marks) A chemical engineer is designing the production process for a new product. The chemical reaction that produces the product may have higher or lower yield, depending on the temperature and the stirring rate in the vessel in which the reaction takes place. The engineer decides to investigate the effects of combinations of two temperatures (50 degrees Celsius and 60 degrees Celsius) and three stirring rates (60 rpm, 90 rpm, and 120 rpm) on the yield of the process. Two batches of the feedstock will be processed at each combination of temperature and stirring rate. a) How many factors are there in this experiment? How many treatments? Identify each of the treatments. How many experimental units (batches of feedstock) does the experiment require? b) Outline in graphic form the design of an appropriate experiment. c) Use Table B starting at line 128 to carry out the randomization required by your design and state the result. Choose your labels beginning at one, not zero. a) There are two factors: temperature and stirring rate, and six treatments, consisting of the various temperature stirring rate combinations: 50 degrees and 60 rpm, 50 degrees and 90 rpm, etc. Twelve batches are needed (in order to have at least two replicates at each treatment). b) Group 1 Treatment 1 2 batches 50 C / 60 rpm Group 2 Treatment 2 2 batches 50 C / 90 rpm Group 3 Treatment 3 Random 2 batches 50 C / 120 rpm Observe Assignment yield Group 4 Treatment 4 2 batches 60 C / 60 rpm Group 5 Treatment 5 2 batches 60 C / 90 rpm Group 6 Treatment 6 2 batches 60 C / 120 rpm c) From line 128, the first 10 numbers (between 01 and 12) are 06, 09, 03, 05, 04, 07, 02, 08, 10, 11. So the 6th and 9th batches will receive treatment 1; batches 3 and 5 will be processed with treatment 2, etc. [Number the treatment combinations 1 to 6, in any order you prefer.] Page 4
5 Question #5 (12 Marks) Here s more evidence that our intuition about chance behaviour iss not very accurate. A six-sided die has four green and two red faces, all equally probable. Psychologists asked students to say which of these colour sequences is most likely to come up at the beginningg of a long sett of rolls of this die: RGRRR RGRRRG GRRRRR More than 60% chose the second sequence. What is the correct probability off each sequence? Page 5
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