Question

In: Statistics and Probability

In estimating the average price of a gallon of gasoline in a region we plan to...

In estimating the average price of a gallon of gasoline in a region we plan to select a random sample (independent and identically distributed) of size 10. Let X1, X2, ... , X10 denote the selected sample. The two estimators for estimating the average price, μ , are:

U1 = (X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 +X9 + X10)/10

U2 = (X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 )/8 + X1 - X2 .

a. which of the above estimators are unbiased? Fully justify your answer.

b. Using the mean square error criterion, determine which estimator is better.

Solutions

Expert Solution


Related Solutions

In estimating the average price of a gallon of gasoline in a region we plan to...
In estimating the average price of a gallon of gasoline in a region we plan to select a random sample (independent and identically distributed) of size 10. Let X1 , X2 , ... , X10 denote the selected sample. The four estimators for estimating the average price, mu, are: U1 = ( X1 + X2 + ... + X10 ) /10 U2 = ( X1 + X2 + ... + X8 ) /8 + X10 - X9 U3 = (...
In estimating the average price of a gallon of gasoline in a region we plan to...
In estimating the average price of a gallon of gasoline in a region we plan to select a random sample (independent and identically distributed) of size 10. Let X1, X2, ... , X10 denote the selected sample. The two estimators for estimating the average price, μ, are: U1 = (X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 +X9 + X10)/10 U2 = (X1 + X2 + X3 + X4 + X5 + X6...
Suppose that you are interested in estimating the average number of miles per gallon of gasoline...
Suppose that you are interested in estimating the average number of miles per gallon of gasoline your car can get. You calculate the miles per gallon for each of the next twenty-five times you fill the tank. Suppose that in truth, the values for your car are bell-shaped, with a mean of 20 miles per gallon and a standard deviation of 1. Find the possible sample means you are likely to get based on your sample of twenty-five observations. Consider...
The average price for a gallon of gasoline in the United States is 3.75 and in...
The average price for a gallon of gasoline in the United States is 3.75 and in Russia it is 3.37. Assume these averages are the population means in the two countries and that the probability distributions are normally distributed with a standard deviation of .25 in the United States and a standard deviation of .20 in Russia. a. What is the probability that a randomly selected gas station in the United States charges less than ________ per gallon (to 4...
The average price for a gallon of gasoline in the United States is $3.74 and in...
The average price for a gallon of gasoline in the United States is $3.74 and in Russia it is $3.4. Assume these averages are the population means in the two countries and that the probability distributions are normally distributed with a standard deviation of $0.25 in the United States and a standard deviation of $0.20 in Russia. a. What is the probability that a randomly selected gas station in the United States charges less than $3.65 per gallon (to 4...
The average price of a gallon of unleaded regular gasoline was reported to be $3.44 in...
The average price of a gallon of unleaded regular gasoline was reported to be $3.44 in northern Kentucky. Use this price as the population mean, and assume the population standard deviation is $0.30. What is the probability that the mean price for a sample of 50 service stations is within ±$.06 of the population mean? What is the probability that the mean price for a sample of 100 service stations is within ±$.06 of the population mean? The Wall Street...
1. The average price of a gallon of gasoline (regular unleaded) in 1976 was $0.64. In...
1. The average price of a gallon of gasoline (regular unleaded) in 1976 was $0.64. In 1998 it was $1.06. The CPI factor in 1976 is 56.9 and the CPI factor in 1998 is 163.0.   Convert the 1976 price to constant 1998 dollars. Was gas more expensive in 1976 or in 1998? Choose two correct answers. Question 3 options: Gas was more expensive in 1998. Gas was more expensive in 1976. The 1976 price in 1998 constant dollars is  $1.83. The...
Oil and Gas Prices The average gasoline price per gallon (in cities) and the cost of...
Oil and Gas Prices The average gasoline price per gallon (in cities) and the cost of a barrel of oil are shown below for a random selection of weeks in 2015 . Oil ( $ ) Gasoline ( $ ) 55.78 2.654 41.96 2.269 52.08 2.445 57.28 2.710 58.15 2.805 67.59 3.071 The correlation coefficient for the data is =r0.978 and =α0.01 . Should regression analysis be done? The regression analysis should not be done. The regression analysis should be...
Oil and Gas Prices The average gasoline price per gallon (in cities) and the cost of...
Oil and Gas Prices The average gasoline price per gallon (in cities) and the cost of a barrel of oil are shown below for a random selection of weeks in 2015. Oil ($) Gasoline ($) 55.78 2.654 41.96 2.269 52.08 2.445 57.28 2.710 58.15 2.805 67.59 3.071
Oil and Gas Prices The average gasoline price per gallon (in cities) and the cost of...
Oil and Gas Prices The average gasoline price per gallon (in cities) and the cost of a barrel of oil are shown below for a random selection of weeks from 2015. Oil $47.79 $44.62 $81.08 $43.67 $40.58 $48.64 Gasoline 2.638 2.636 2.944 2.528 2.623 2.682 1) The correlation coefficient for the data is r = 0.951 and a = 0.01. Should regression analysis be done? a) The regression analysis should not be done or b) The regression analysis should be...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT