Part A: There is a population of five people. They were each asked how many movies they saw in the last year. Amy saw one (1), Bob saw seven (7), Clara saw thirteen (13), Dora saw nineteen (19), and Earl saw twenty-five (25). Looking at every single possible sample of size three (with replacement). First column will be a list of every single sample (e.g., Amy, Amy, and Amy – or AAA – Amy, Amy, and Bob – or AAB – et cetera). The second column will list the mean of each sample.The third column will list the variance of each sample (using N in the denominator); and the fourth column will list the variance of each sample (using N-1 as the denominator). Calculate the means of the last three columns. To calculate the averages of the columns, put the data in a frequency table and then calculate the mean using the table. Calculate the variance of the population. Look at the values of the numbers. Which one of these means is special? Why? This will have six distinct parts: 1) the mean of the sample means; 2) the mean of the variances (using n in the formula’s denominator); 3) the mean of the variances (using n-1 in the formula’s denominator); 4) the variance of the population; 5) an explanation of what the averages are (besides just saying they are the averages of the columns); 6) an explanation of what you learn comparing these numbers and why this knowledge is important. Part B: You’ve already calculated the average for each sample along with the variance for each sample using N and the variance for each sample using N-1 (which is an estimate of the population variance). These two columns of the sample variance will not be used in this extra credit. Part 1) Make a graph where the x-axis is the value of and the y-axis is the frequency of that value. Part 2) Explain what this is a graph of. Part 3) calculate the average of the of the ’s which is labeled E(), in other words, it is the expected value of the averages, or if you will, the average of the averages. This is also called the expected value of the sampling distribution. Part 4) Show that E() = m. In other words, calculate the population average and show that it equals what you got in Part 3. Part 5) Explain why Part 4 is important. Part 6) Calculate the standard deviation of the ’s. This is called the standard error of the sampling distribution. Part 7) Show that = . In other words, calculate the population standard deviation and divide it by the square root of the sample size (not the population size). Show that this equals what you got in Part 6. Part 8) Explain why Part 7 is important.
Part A:
There is a population of five people. They were each asked how many movies they saw in the last year. Amy saw one (1), Bob saw seven (7), Clara saw thirteen (13), Dora saw nineteen (19), and Earl saw twenty-five (25). Looking at every single possible sample of size three (with replacement). First column will be a list of every single sample (e.g., Amy, Amy, and Amy – or AAA – Amy, Amy, and Bob – or AAB – et cetera). The second column will list the
Calculate the means of the last three columns. To calculate the averages of the columns, put the data in a frequency table and then calculate the mean using the table.
Calculate the variance of the population.
Look at the values of the numbers. Which one of these means is special? Why?
This will have six distinct parts: 1) the mean of the sample means; 2) the mean of the variances (using n in the formula’s denominator); 3) the mean of the variances (using n-1 in the formula’s denominator); 4) the variance of the population; 5) an explanation of what the averages are (besides just saying they are the averages of the columns); 6) an explanation of what you learn comparing these numbers and why this knowledge is important.
Part B:
You’ve already calculated the average for each sample along with the variance for each sample using N and the variance for each sample using N-1 (which is an estimate of the population variance). These two columns of the sample variance will not be used in this extra credit.
Part 1) Make a graph where the x-axis is the value of and the y-axis is the frequency of that value.
Part 2) Explain what this is a graph of.
Part 3) calculate the average of the of the ’s which is labeled E(), in other words, it is the
Part 4) Show that E() = m. In other words, calculate the population average and show that it equals what you got in Part 3.
Part 5) Explain why Part 4 is important.
Part 6) Calculate the standard deviation of the ’s. This is called the standard error of the sampling distribution.
Part 7) Show that = . In other words, calculate the population standard deviation and divide it by the square root of the sample size (not the population size). Show that this equals what you got in Part 6.
Part 8) Explain why Part 7 is important.
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