Mathematics & Statistics Texas Tech University Kent Pearce Department of Mathematics and Statistics Texas Tech University Lubbock, Texas 79409-1042 Voice: (806)742-2566 x 226 FAX: (806)742-1112 Email: kent.pearce@ttu.edu

Homework & Groupwork
Mathematical Statistics for Scientists and Engineers
 Math 3342-001 Summer II 2001 Johnson, Richard Miller and Freund's Probability and Statistics for Engineers Prentice Hall Upper Saddle River, NJ 2000

 Homework #1 Chapter 1: 2, 6 Chapter 2: 2-3, 5, 7, 9-10, 14-15, 21, 28-29, 33-36, 39-40, 44-45, 49 Due: Monday, July 16 Groupwork #1 Choose a population of units. Choose a population variable. Collect two samples from the population, each of size 16. Written Description: a) Describe the population of units and the population variable. b) Describe how, where and when the samples were collected. Statistical Presentation: a) dot plots of the sample data sets b) frequency distributions of the sample data sets and graphs c) cummulative frequency distributions of the sample sets data and graphs d) percent frequency distributions of the sample data sets and graphs e) box plots of the sample data sets f) means, medians and variances for each of the sample data sets Due: Monday, July 16
 Homework #2 Chapter 3: 8, 17-19, 21, 23, 28, 30-32, 35, 46, 48, 51, 59, 64, 71, 73, 78 Chapter 4: 2, 3, 5, 10abcd, 13, 14, 17 Due: Tuesday, July 24 Groupwork #2 Consider the data set "bodyfat.txt" from the library "lib.stat.cmu.edu" which reports body fat measurements for 252 men. Define the following stratification of the data set. Ages 20-29 Ages 30-39 Ages 40-49 Ages 50-50 Ages 60-69 Ages 70-79 Select two strata from the dataset and assess for each strata the following: Define for each strata the following events: Let BF1 be the set of men such that their percent body fat is less than or equal to 8.0%. Let BF2 be the set of men such that their percent body fat is more than 8% and less than or equal to 22.0%. Let BF3 be the set of men such that their percent body fat is more than 22.0%. Let W1 be the set of men such that their weight is less than or equal to 170.00 lbs. Let W2 be the set of men such that their weight is more than or equal to 225.00 lbs. Construct a contingency table for percent body fat vs weight as defined by the above events for each of the (two) selected strata. Find for each of the (two) selected strata the following and compare results for the strata: a) P(BF1), P(BF2), P(BF3), P(W1), P(W2) b) P(BF1 | W1), P(BF1 | W2), P(BF2 | W1), P(BF2 | W2), P(BF3 | W1), P(BF3 | W2) c) Let V be the set of men that are vegitarians. Suppose that is is appriori known that: P(V | BF1) = 0.23 P(V | BF2) = 0.16 P(V | BF3) = 0.09 Find P(V). Further find, P(BF1 | V). Due: Tuesday, July 24
 Homework #3 Chapter 4: 18, 20, 23, 26, 30, 35, 39, 42, 44, 50, 53, 55, 57, 60, 64, 70 Due: Monday, July 30 Groupwork #3 a) Consider the data sets Math Placement Scores June 18, 2000 and Math Placement Scores July 30, 2000. For each data set: Select a random sample (use a random number table) of size 80. Use the empirical sample to estimate the probablity distribution for the placement code (values 1 - 7). Find the mean and standard deviation of the probability distribution. Find/Estimate the probability that given a sample of size 100 that no more that 12 will have a code 1. Due: Monday, July 30
 Homework #4 Chapter 5: 24-25, 27, 33, 37, 42, 46, 51, 53, 55, 59, 64-65, 71-72, 76, 78, 89-92 Chapter 6: 5-6, 11-12, 15, 17 Due: Monday, August 6 Groupwork #4 There are two new data sets available from the dataset library at CMU. These are data sets about the effects of cloud seeding on rainfall and about regression estimates on pollution. Select one of the data sets: Find a continuous random variable for which a normal-scores plot strongly suggests that the data is normal. (If you choose the cloud seeding data set, then subselect either the seeded or the unseeded data for one of the locations). Calculate the mean and variance for the data. Select 20 (random) samples of size 10 from the data set; calculate the mean for each sample. Calculate the mean and variance of the above 20 sample means. Let y denote the 5th above obtained sample mean of size 10. Let X denote the random variable of sampling means of size 10. Apply Theorem 6.2 to find the P(X > y). Due: Monday, August 6

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