TheSanityAnnex
03-23-2008, 08:24 PM
20 bucks to the first person to finish via paypal. And no, I won't just take the answers and not pay, I will pay. Kori can ban my ass if the first to finish (correctly) doesn't receive their money. I'm pretty much offering Baseline Bum 20 bucks cause he seems good at stats.
(1) Suppose you are interested in estimating the actual amount of Pepsi that is placed in 2-liter bottles. Pepsi-Co has informed you that the population of Pepsi bottles is distributed normally with a mean of 2.00 liters and a standard deviation of 0.05 liters. What is the probability that that one bottle drawn at random will contain more than 2.07 liters or less than 1.97 liters?
For the next two questions, suppose you are interested in Coca-Cola instead of Pepsi. However, this time you do not know the sample mean for the Coke bottles you are testing.
(2) Suppose that the population standard deviation for the amount of liquid in a Coke bottle is 0.03. Suppose you take a sample of 20 bottles drawn at random whose sample mean is 1.02. Find a 90% confidence interval for the true population mean. (Hint: use normal distribution)
(3) Suppose you do not know the population standard deviation for the amount of liquid in a Coke bottle. Instead, you take a sample of 20 bottles drawn at random and find that the sample mean is 1.02 and the sample standard deviation is 0.03. Find a 90% confidence interval for the true population mean. (Hint: use Student’s t distribution)
(4) The personnel department of a business would like to estimate the family dental expenses of its employees to determine the feasibility of providing a dental insurance plan. A random sample of 10 employees reveals the following family dental expenses (in dollars) for the preceding year:
110, 362, 246, 85, 510, 208, 173, 425, 316, 179
Find a 95% confidence interval for the population proportion of family dental expenses that are above $300 (Hint: use the Normal distribution for proportions).
(5) Suppose you are performing a blind taste test for carbonated beverages and you want to see how Dr. Pepper scores against other soft drinks. You ask people to try different soft drinks and then provide a score (out of 100) for Dr. Pepper against the other types of soft drinks. How many people would you have to survey if the mean score is to be estimated within plus or minus 2 of the true population mean when the standard deviation is 15? Use a 94% level of confidence.
(1) Suppose you are interested in estimating the actual amount of Pepsi that is placed in 2-liter bottles. Pepsi-Co has informed you that the population of Pepsi bottles is distributed normally with a mean of 2.00 liters and a standard deviation of 0.05 liters. What is the probability that that one bottle drawn at random will contain more than 2.07 liters or less than 1.97 liters?
For the next two questions, suppose you are interested in Coca-Cola instead of Pepsi. However, this time you do not know the sample mean for the Coke bottles you are testing.
(2) Suppose that the population standard deviation for the amount of liquid in a Coke bottle is 0.03. Suppose you take a sample of 20 bottles drawn at random whose sample mean is 1.02. Find a 90% confidence interval for the true population mean. (Hint: use normal distribution)
(3) Suppose you do not know the population standard deviation for the amount of liquid in a Coke bottle. Instead, you take a sample of 20 bottles drawn at random and find that the sample mean is 1.02 and the sample standard deviation is 0.03. Find a 90% confidence interval for the true population mean. (Hint: use Student’s t distribution)
(4) The personnel department of a business would like to estimate the family dental expenses of its employees to determine the feasibility of providing a dental insurance plan. A random sample of 10 employees reveals the following family dental expenses (in dollars) for the preceding year:
110, 362, 246, 85, 510, 208, 173, 425, 316, 179
Find a 95% confidence interval for the population proportion of family dental expenses that are above $300 (Hint: use the Normal distribution for proportions).
(5) Suppose you are performing a blind taste test for carbonated beverages and you want to see how Dr. Pepper scores against other soft drinks. You ask people to try different soft drinks and then provide a score (out of 100) for Dr. Pepper against the other types of soft drinks. How many people would you have to survey if the mean score is to be estimated within plus or minus 2 of the true population mean when the standard deviation is 15? Use a 94% level of confidence.