# Which of the following statistics are unbiased estimators

1) Which of the following statistics are unbiased estimators of population parameters? Sample range used to estimate apopulation range. Choose the correct answer below. Select all that apply.A.Sample range used to estimate a population range.B.Sample proportion used to estimate a population proportion.C.Sample standard deviation used to estimate a population standard deviation.D.Sample variance used to estimate a population variance.E.Sample median used to estimate a population median.F.Sample mean used to estimate a population mean.2) Three randomly selected households are surveyed. The numbers of people in the households are 2,6, and 13. Assume that samples of size n equals=2 are randomly selected with replacement from the population of2, 6, and 13.Listed below are the nine different samples. Complete parts (a) through (c).2,2???2,6??? 2,13???6,2???6,6???6,13???13,2???13,6???13,13Answer a,b,ca. Find the median of each of the nine samples, then summarize the sampling distribution of the medians in the format of a tablerepresenting the probability distribution of the distinct median values.b. Compare the population median to the mean of the sample medians.c. Do the sample medians target the value of the population median? In general, do sample medians make good estimators ofpopulation medians? Why or why not? _______________________________________________________________________________3) Three randomly selected households are surveyed. The numbers of people in the households are3, 4, and 11. Assume that samples of size N equals=2 are randomly selected with replacement from the population of3, 4, and 11.Listed below are the nine different samples.3,3???3,4???3,11???4,3???4,4???4,11???11,3???11,4???11,11Answer a,b,ca.Find the variance of each of the nine samples, then summarize the sampling distribution of the variances in the format of atable representing the probability distribution of the distinct variance value. Find S2 and probability for eachb. Compare the population variance to the mean of the sample variances. c. Do the sample variances target the value of the population variance? In general, do sample variances make good estimatorsof population variances? Why or why not? _________________________________________________________________________________________________________________ 4) An ice company was in business for only three days. Here are the numbers of phone calls received on each of those days: 8,3, 2. 1. Assume that samples of size 2 are randomly selected with replacement from this population of three values. List the different possible samples and find the mean of each of them. Select the correct choice below and fill in the answerboxes within your choice. Answer a,b,c,da. After listing the possible samples and finding the mean of each sample, use a table to describe the sampling distributionof the sample means.b. Identify the probability of each sample and describe the sampling distribution of sample meansc. Find the mean of the sampling distribution.d. Is the mean of the sampling distribution [from part (c)] equal to the mean of the population of the three listed values?If so, are those means always equal?Calculate the mean of the population of the three listed values. _______________________________________________________________________________5) The assets (in billions of dollars) of the four wealthiest people in a particular country are 45, 32, 17, 15. Assume that samples of size 2 are randomly selected with replacement from this population of four values.Answer a,b,ca. After listing the possible samples and finding the mean of each sample, use a table to describe the sampling distributionof the sample means.b. b. Find the mean of the sampling distribution.c. c. Is the mean of the sampling distribution [from part (b)] equal to the mean of the population of the four listed values?If so, are those means always equal? 6) The ages (years) of three government officials when they died in office were 56, 46, and 60.Complete parts (a) through (d).a. Assuming that 2 of the ages are randomly selected with replacement, list the different possible samples.b. Find the range of each of the samples, then summarize the sampling distribution of the ranges in the format of a tablerepresenting the probability distribution.c. Compare the population range to the mean of the sample ranges. d. Do the sample ranges target the value of the population range? In general, do sample ranges make good estimators ofpopulation ranges? Why or why not?7) Three randomly selected households are surveyed. The numbers of people in the households are 1, 3, and 8.Assume that samples of size n equals=2 are randomly selected with replacement from the population of 1, 3, and 8.Construct a probability distribution table that describes the sampling distribution of the proportion of even numbers whensamples of sizes n equals=2 are randomly selected. Does the mean of the sample proportions equal the proportion ofeven numbers in the population? Do the sample proportions target the value of the population proportion? Does thesample proportion make a good estimator of the population proportion? Listed below are the nine possible samples.1,1???1,3???1,8???3,1???3,3???3,8???8,1???8,3???8,8Do a,b,c,d a. Construct the probability distribution table. Showing Sample Proportion and Probability b. Also Determine if the mean of the sample proportions is equal to the proportion of odd numbers in thepopulation. Find the mean of the sample proportions. Calculate the mean of the sample proportions,rounding to three decimal places. C, c.d. Determine if the sample proportions target the value of the population proportion. Determine if the sample proportion makes a good estimator of the population proportion. 8. A genetics experiment involves a population of fruit flies consisting of 3 males named Carlos, Donald, and Eric and 1 femalenamed Fran.Assume that two fruit flies are randomly selected with replacement.Answer a,b,ca. After listing the possible samples and finding the proportion of femalesin each sample, use a table to describe the sampling distribution of the proportion of females. b. Find the mean of the sampling distribution.c. Is the mean of the sampling distribution [from part (b)] equal to the population proportion of males?If so, does the mean of the sampling distribution of proportions always equal the population proportion?Calculate the population proportion of males.