(a) What is the best point estimate, based on the sample, to use for the population mean? (b) For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value for the 90% confidence interval for the population mean. (In the table, Z refers to a standard normal distribution, and t refers to at distribution.) Could use Sampling scenario Unclear either Z ort The sample has size 75, and it is from a non-normally distributed population with a known standard deviation of 75. The sample has size 14, and it is from a normally distributed population with an unknown standard deviation. The sample has size 95, and it is from a non-normally distributed population.

a)Determine the mean of sample means distribution b) Determine the standard deviation (standard error) of sample means distributionc) Draw a Normal (bell-shaped) graph for sample means distribution byhand on a paper showing x and y axes without any values marked on them. However,label the values of mean and standard deviation as described below. The adult male heights in a country vary normally with mean of 70 inches and standarddeviation of 4 inches. We draw many samples of size 100 from the above populationusing repeated random sampling and record the mean height for each sample to constitutea sample means distribution (?̅ -distribution). Do the above for the distribution.

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You would like to construct a 95% confidence interval to estimate the population mean annual income for people over age 40 in your state. You choose a random sample of such incomes and compute the mean of the sample as 40,346 dollars with a standard deviation of 7757 dollars. (a) What is the best point estimate, based on the sample, to use for the population mean? dollars G (b) For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value for the 95% confidence interval for the population mean. (In the table, Z refers to a standard normal distribution, and refers to a t distribution.) Sampling scenario z t Could use either Z or / Unclear The sample has size 14, and it is from a normally distributed population with an unknown standard deviation. о о The sample has size 17, and it is from a population with a distribution about which we know very little. O о The sample has size 110, and it is from a non-normally distributed…