CHAPTER 3 EXERCISES (Set 2)
- 1. Buy here: http://student.land/chapter-3-exercises-set-2/ CHAPTER 3 EXERCISES (Set 2) 1. Male Angus beef cattle weights are distributed N(1156, 84) (in lbs.). a. If we randomly sample 9 male Angus cows, what is the probability that their average weight will be 1220 lbs. or more? Use Minitab to solve this inputting the actual population parameters, then use Minitab to show that the probability obtained by using the corresponding standardized score is the same. b. If we randomly sample 16 male Angus cows, what is the probability that their average weight will be 1220 lbs. or more? Use Minitab to solve this inputting the actual population parameters, then use Minitab to show that the probability obtained by using the corresponding standardized score is the same. c. If we randomly sample 49 male Angus cows, will the probability that their average weight is 1220 lbs. or more be greater or less than the probability from b? (Try to answer without calculating the probability.) 2. According to the US Census Bureau, commuting times for Indiana residents have a mean of 24 minutes and a population standard deviation of 12 minutes. a. If one Indiana resident is selected at random, what is the approximately probability that his/her commute time is greater than 26 minutes?
- 2. b. If 36 Indiana residents are selected at random, what is the approximate probability that their average commute time will be greater than 26 minutes? 3. We are managing a large soy bean farm. To estimate our revenues for the coming year, we need to estimate our crop yield. Soy bean yields are measured by pods/plant. We are planning for a yield of 40 pods/plant. We take a random sample of 36 soy bean plants and get a sample mean yield of 38.5 pods/plant with asample standard deviation of 4.8 pods/plant. Assuming that our population pods/plant is 40, what is the probability of obtaining the sample we got or one that varies more in the same direction from the assumed mean? (Use Minitab - note that the probability comes from a t distribution.) 4. An exercise on sampling distributions for sample means: a. To study sampling from the population of Chinook salmon (the largest species of Pacific salmon), use Minitab to draw 100 random numbers from N(44,12), the distribution of Chinook salmon weights. Have Minitab compute the mean and standard deviation of the sample. How do these statistics compare to the corresponding population parameters? Compute the 5-number summary and note in particular the Maximum and Minimum. For the sampling use: Calc -> Random Data -> Normal -> Number of rows to generate: 100 -> Store in column(s): c1 -> Enter mean and standard deviation
- 3. b. Now, use Minitab to simulate taking 50 samples of size 100 from this distribution. Use Stat - > Basic Stat to compute the mean of each of the 50 samples. (The means will be recorded in the Project Sheet.) Note how each of these means compares to the population mean. For the sampling, use the above with: Store in column(s): c1 – c50. For the means, use Stat -> Basic Statistics -> Display Descriptive Statistics -> select Mean only -> Variables: c1 – c50. c. It is these means, not the numbers from the population, that are distributed by the sampling distribution for means for this sampling situation (which is means from sample size 100 from N(44, 12)). To see how this distribution differs from the population, enter (or copy and paste) these 50 means into the Minitab worksheet, then calculate the mean and standard deviation of these 50 numbers. The mean should be approximately 44. The standard deviation should be approximately 1.2. Explain why? Compute the 5-number summary of these 50 means and note their Maximum and Minimum. How does the spread of these means compare to the spread of numbers from your sample in part a? Why is this spread so much narrower? For full credit for Exercise 4, copy and paste from your Project Sheet your 50 sample means along with the other requested calculations. Do not print out your Worksheet which contains the actual samples.