introduction to probability and statistics homwork project Collect pennies in the amount of $2. Do not obtain rolls of pennies from a bank because many such rolls will consist solely of new pennies. Treat these 200 pennies as your population. Determine the ages, in years, of all these pennies. Calculate the mean and standard deviation of these ages and denote them by and , respectively. a. Take a random sample of 30 pennies from these 200. Find the average age of these 30 pennies, which is the value of x. Perform a test with the null hypothesis that is equal to the value obtained for all 200 pennies and the alternative hypothesis that is greater than this value. Use a significance level of .10. b. Suppose you repeat the procedure of part a five more times. How many times would you expect to reject the null hypothesis? Now actually repeat the procedure of part a five more times, making sure that you put the 30 pennies selected each time back in the population and that you mix all pennies well before taking a sample. How many times did you reject the null hypothesis? Note that you can enter the ages of these 200 pennies in a technology. c. Repeat parts a and b for a sample size of 40. Did you reject the null hypothesis more often with a sample size of 30 or a sample size of 40? MAKE SURE YOU ARE PUTTING A SQ ROOT IN THE Z FORMULA -Z=(XBAR-MU)/(SIGMA/SQRT(N)

introduction to probability and statistics homwork project Collect pennies in the amount of $2. Do not obtain rolls of pennies from a bank because many such rolls will consist solely of new pennies. Treat these 200 pennies as your population. Determine the ages, in years, of all these pennies. Calculate the mean and standard deviation of these ages and denote them by and , respectively. a. Take a random sample of 30 pennies from these 200. Find the average age of these 30 pennies, which is the value of x. Perform a test with the null hypothesis that is equal to the value obtained for all 200 pennies and the alternative hypothesis that is greater than this value. Use a significance level of .10. b. Suppose you repeat the procedure of part a five more times. How many times would you expect to reject the null hypothesis? Now actually repeat the procedure of part a five more times, making sure that you put the 30 pennies selected each time back in the population and that you mix all pennies well before taking a sample. How many times did you reject the null hypothesis? Note that you can enter the ages of these 200 pennies in a technology. c. Repeat parts a and b for a sample size of 40. Did you reject the null hypothesis more often with a sample size of 30 or a sample size of 40? MAKE SURE YOU ARE PUTTING A SQ ROOT IN THE Z FORMULA -Z=(XBAR-MU)/(SIGMA/SQRT(N)