1. Sampling Distribution. Distinguish between a distribution of sample means and a distribution of sample proportions.

The distribution of sample means is the distribution that results when we find the means of all possible samples of a given size (Bennett et al., 2018). The distribution of sample proportions is the percentage of a population.

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.

The sampling error is the error introduced because a random sample is used to estimate a population parameter. It does not include other sources of error, such as biased sampling, bad survey questions, or recording mistakes (Bennett et al., 2018). The sampling error decreases when there is a larger sample size. When there is a large sample size it gives a closer interpretation of what they are sampling. It will be closer to the correct data.

3. Sample Means and Proportions. What is a sample mean? What is a sample proportion? Summarize the notation used for these statistics.

A sample mean is an average of a set of data. The sample proportion is a random variable that varies from sample to sample in a way that cannot be predicted with certainty. "n" for sample size and "p" for proportion.

4. Sample Size. How does the sample size affect how close to normal a distribution of either sample means or sample proportions will be? What are the means and standard deviations of the distributions in each case?

5. Sampling Distribution. I selected three different samples of size n=10 n equals 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 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=6.7 x bar, equals 6.7 pounds and p=0.45, p hat , equals , 0.45 , comma or 45% showed signs of jaundice.

19. Sampling Distribution. A quarterback threw 1 interception in his first game, 2 interceptions in his second game, and 5 interceptions 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?