Suppose we are interested in the proportion of adults in the U.S. with a bachelor’s degree or higher. We randomly select 5000 adults in order to estimate this proportion. Use this information to...

Suppose we are interested in the proportion of adults in the U.S. with a bachelor’s degree or higher. We randomly select 5000 adults in order to estimate this proportion. Use this information to answer questions 1-4. 1) What is the population? 2) What is the sample? 3) What is the parameter? 4) What is the statistic? 5) In the graph below, the sampling distribution for three statistics that could be used to estimate the parameter  is presented. Which statistic would typically give you the best estimate? Explain.Suppose the number of cell phone calls made or received per day by cell phone users follows a normal distribution with a mean of 13.1 and a standard deviation of 4.3. Use this information to answer questions 6-9. 6) Find Px 12. 7) Find  x for a sample of size 100. 8) Find  x for a sample of size 100. 9) Find Px 12 for a sample of size 100. The population mean yearly income of all adult residents in the state of Kentucky is $48,000 with a standard deviation of $9000. Use this information to answer questions 10-13. 10) Can you find Px  52,000 ? 11) Find  x for a sample of size 50. 12) Find  x for a sample of size 50. 13) Find Px  52,000 for a sample of size 50. 14) Explain why we can find the probability in question 6, 9, and 13 but not in question 10? The proportion of graduating high school students who can read at an eighth grade level is 65%. Use this information to answer questions 15-17. 15) Find  p ˆ for a sample of size 75. 16) Find  p ˆ for a sample of size 75. 17) Find P0.62  p ˆ  0.68 for a sample of size 75.




18) The outcome X when rolling a die is a discrete probability distribution (this question should be done by hand using the information presented in section III. B.) a. Identify this discrete probability distribution. b. Calculate the mean for the distribution. c. Calculate the standard deviation for the distribution. d. Identify the median of the distribution (Hint: this is a uniform distribution which is also symmetric, so think about how the mean and median compare in the distribution). 19) For the Student Survey Data you should have created a Row Mean column representing the mean of Roll1 – Roll10 for each student. This quantity represents a sample mean. a. What is the mean of the Row Mean (sample means) column? b. Is this estimate centered about the parameter of interest (mean/median in question 18)? c. What is the standard deviation of the Row Mean (sample means) column? d. Is there a small amount of variability in this estimate? 20) You should have also created a Row Median column representing the median of Roll1 – Roll10 for each student. a. What is the mean of the Row Median (sample medians) column? b. Is this estimate centered about the parameter of interest (mean/median in question 18)? c. What is the standard deviation of the Row Median (sample medians) column? d. Is there a small amount of variability in this estimate? 21) Looking at questions 19 and 20, does the sample mean or sample median typically give a better estimate for the center of the distribution? Explain. 22) Look at the descriptive statistics for the mean of the simulated data (sampling distribution from right skewed population) for samples of size 1, 10, and 30. Keep in mind that this is simulated data which is like taking a random sample. Therefore, each time data is simulated, you will get slightly different outcomes. The overall pattern, however, will remain consistent. a. What is the mean when the sample size is 1. b. What is the mean when the sample size is 10. c. What is the mean when the sample size is 30. d. Is the mean of the sampling distribution close to the mean of the population (remember the population mean is 1) in each case (a, b, and c above)? e. Is the mean of the sampling distribution effected by the increase in sample size? f. What is the standard deviation when the sample size is 1. g. What is the standard deviation when the sample size is 10. h. What is the standard deviation when the sample size is 30. i. What effect does the change in sample size have on the standard deviation of the sampling distribution (standard error)? 23) Identify the shape of the sampling distributions for sample means (with an underlying distribution that is right skewed) for each sample size. Use the histograms and descriptive statistics (compare mean and median) to explain how you determined the shape in each case. a. When sample size is 1 b. When sample size is 10 c. When sample size is 30 24) What do the shapes of the sampling distributions identified in question 23 tell you about how sample size effects the distribution of a statistic (Hint: think about the Central Limit Theorem)?