M6-223-Assignment

Statistical Literacy and Critical Thinking 1. Sampling Distribution. Distinguish between a distribution of sample means and a distribution of sample proportions. 2. Sampling Error. 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 sample sizes? Explain. 3. Sample Means and Proportions. What is a sample mean? What is a sample proportion? Summarize 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 pro-portions will be? What are the means and standard deviations of the distributions in each case? Does It Make Sense? For Exercises 5–8, determine whether the statement makes 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. Sampling 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 Americans 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 pro-portion 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 =6.7 pounds and pn =0.45, or 45% showed signs of jaundice.

19 . Sampl ing Distribut ion. A quarterback threw 1 interception in his first game, 2 interceptions in his second game, and 5 inter-ceptions in his third game, and then he retired. Consider the values 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?