Complete the following chapter review exercise out of your textbook:
- Exercises 1-8 (pp. 277-278)
In these exercises, you will think critically about sampling distributions and judge the reasonableness of several example scenarios.
Statistical Literacy and Critical Thinking
1. Sampling Distribution. Distinguish between a distribution of sample means and a distribution of sample proportion.
2. Sampling Errors. What is a sampling error? How does it differ from other sources of error? In general, how does the sampling error increase or decrease with larger sampling sizes. Explain.
3. Sample Means and Proportion. What is a sample mean? What is a sample proportion? Summarizing the notation used for these statistics.
4. Sample Size. How does the sample size affect how close to normal a distribution of either sample means or sample proportion will be? What are the means and standard deviations of the distribution in each case?
Does it make sense? For exercise 5-8 determine whether the statements make sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly. Not all of these statements have definitive answers, so your explanation is more important than your chosen answer.
5. Sample Distribution. I selected three different samples of size n = 10 drawn from the 1500 students at my school, and with these I constructed the sampling distribution.
6. Sample Proportion. Nielsen Media Research determined the precise proportion of all American watching the Super Bowl by conducting a survey of a few thousand households.
7. Sample Reliability. Although Nielsen surveys only a few thousand households out of the millions that own TVs, they have a good chance of getting an accurate estimate of the proportion of the population watching the Super Bowl.
8. Notation. Our study measured the birth weights and incidence of jaundice among a sample of babies born at our hospital, and we found x with a line over it =6.7 pounds and ^p =0.45, or 45% showed sign of jaundice.
- Exercise 19 (p. 278)
In this exercise, which dovetails with the topic of this week’s discussion topic, you will compute means as well as think critically.
Sampling Distribution. A quarterback threw 1 interception in first game, 2 interceptions in his second game, and 5 interceptions in his third game, and then he retired. Consider the value 1, 2, and 5 to be a population. Assume that samples of size 2 are randomly selected (with replacement) from the population.
a. list the 9 different possible samples, and find the mean of each sample.
b. What is the mean of the sample means from part (a)?
c. Is the mean of the sampling distribution from part (b) equal to the mean of the population of the three listed values? Are those means always equal?
You will submit a 1-page Microsoft Word document with your answers to the questions. You do not need to submit an Excel document.