Deck 27: Estimation and Sample Size Determination for Finite Populations

Question 1

TABLE 8-18
A wealthy real estate investor wants to decide whether it is a good investment to build a high-end shopping complex in a suburban county in Chicago.His main concern is the total market value of the 3,605 houses in the suburban county.He commissioned a statistical consulting group to take a sample of 200 houses and obtained a sample mean market price of $225,000 and a sample standard deviation of $38,700.The consulting group also found out that the mean differences between market prices and appraised prices was $125,000 with a standard deviation of $3,400.Also the proportion of houses in the sample that are appraised for higher than the market prices is 0.24.
Referring to Table 8-18,what will be the 90% confidence interval for the total market price of the houses in the suburban county constructed by the consulting group?

Answer 1

$795,278,945.08 to $826,971,054.92

Question 2

TABLE 8-17
A random sample of 100 stores from a large chain of 500 garden supply stores was selected to determine the mean number of lawnmowers sold at an end-of-season clearance sale.The sample results indicated a mean of 6 and a standard deviation of 2 lawnmowers sold.A 95% confidence interval (5.623 to 6.377)was established based on these results.
True or False: Referring to Table 8-17,if the population had consisted of 400 stores,the confidence interval estimate of the mean with finite population correction would have been wider in range.

Answer 2

False

Question 3

TABLE 8-17
A random sample of 100 stores from a large chain of 500 garden supply stores was selected to determine the mean number of lawnmowers sold at an end-of-season clearance sale.The sample results indicated a mean of 6 and a standard deviation of 2 lawnmowers sold.A 95% confidence interval (5.623 to 6.377)was established based on these results.
True or False: Referring to Table 8-17,if the population had consisted of 1,000 stores,the confidence interval estimate of the mean with finite population correction would have been wider in range.

Answer 3

True

Question 4

TABLE 8-18
A wealthy real estate investor wants to decide whether it is a good investment to build a high-end shopping complex in a suburban county in Chicago.His main concern is the total market value of the 3,605 houses in the suburban county.He commissioned a statistical consulting group to take a sample of 200 houses and obtained a sample mean market price of $225,000 and a sample standard deviation of $38,700.The consulting group also found out that the mean differences between market prices and appraised prices was $125,000 with a standard deviation of $3,400.Also the proportion of houses in the sample that are appraised for higher than the market prices is 0.24.
Referring to Table 8-18,what will be the 90% confidence interval for the total difference between the market prices and appraised prices of the houses in the suburban county constructed by the consulting group?

Question 5

TABLE 8-18
A wealthy real estate investor wants to decide whether it is a good investment to build a high-end shopping complex in a suburban county in Chicago.His main concern is the total market value of the 3,605 houses in the suburban county.He commissioned a statistical consulting group to take a sample of 200 houses and obtained a sample mean market price of $225,000 and a sample standard deviation of $38,700.The consulting group also found out that the mean differences between market prices and appraised prices was $125,000 with a standard deviation of $3,400.Also the proportion of houses in the sample that are appraised for higher than the market prices is 0.24.
Referring to Table 8-18,what will be the 90% confidence interval for the population proportion of houses that will be appraised for higher than the market prices?

Question 6

TABLE 8-18
A wealthy real estate investor wants to decide whether it is a good investment to build a high-end shopping complex in a suburban county in Chicago.His main concern is the total market value of the 3,605 houses in the suburban county.He commissioned a statistical consulting group to take a sample of 200 houses and obtained a sample mean market price of $225,000 and a sample standard deviation of $38,700.The consulting group also found out that the mean differences between market prices and appraised prices was $125,000 with a standard deviation of $3,400.Also the proportion of houses in the sample that are appraised for higher than the market prices is 0.24.
Referring to Table 8-18,if he wants a 95% confidence on estimating the true population mean market price of the houses in the suburban county to be within $10,000,how large a sample will he need?

Question 7

TABLE 8-17
A random sample of 100 stores from a large chain of 500 garden supply stores was selected to determine the mean number of lawnmowers sold at an end-of-season clearance sale.The sample results indicated a mean of 6 and a standard deviation of 2 lawnmowers sold.A 95% confidence interval (5.623 to 6.377)was established based on these results.
True or False: Referring to Table 8-17,of all possible samples of 100 stores taken from the population of 1,000 stores,95% of the confidence intervals developed will contain the true population mean within the interval.

Question 8

TABLE 8-18
A wealthy real estate investor wants to decide whether it is a good investment to build a high-end shopping complex in a suburban county in Chicago.His main concern is the total market value of the 3,605 houses in the suburban county.He commissioned a statistical consulting group to take a sample of 200 houses and obtained a sample mean market price of $225,000 and a sample standard deviation of $38,700.The consulting group also found out that the mean differences between market prices and appraised prices was $125,000 with a standard deviation of $3,400.Also the proportion of houses in the sample that are appraised for higher than the market prices is 0.24.
Referring to Table 8-18,what will be the 90% confidence interval for the mean market price of the houses in the suburban county constructed by the consulting group?

Question 9

TABLE 8-17
A random sample of 100 stores from a large chain of 500 garden supply stores was selected to determine the mean number of lawnmowers sold at an end-of-season clearance sale.The sample results indicated a mean of 6 and a standard deviation of 2 lawnmowers sold.A 95% confidence interval (5.623 to 6.377)was established based on these results.
True or False: Referring to Table 8-17,there are 10 possible samples of 100 stores that can be selected out of the population of 1,000 stores.

Question 10

TABLE 8-17
A random sample of 100 stores from a large chain of 500 garden supply stores was selected to determine the mean number of lawnmowers sold at an end-of-season clearance sale.The sample results indicated a mean of 6 and a standard deviation of 2 lawnmowers sold.A 95% confidence interval (5.623 to 6.377)was established based on these results.
True or False: Referring to Table 8-17,the confidence interval estimate of the mean with finite population correction will be wider in range than confidence interval estimate without finite population correction.

Question 11

TABLE 8-17
A random sample of 100 stores from a large chain of 500 garden supply stores was selected to determine the mean number of lawnmowers sold at an end-of-season clearance sale.The sample results indicated a mean of 6 and a standard deviation of 2 lawnmowers sold.A 95% confidence interval (5.623 to 6.377)was established based on these results.
True or False: Referring to Table 8-17,of all possible samples of 100 stores drawn from the population of 1,000 stores,95% of the sample means will fall between 5.623 and 6.377 lawnmowers.

Question 12

TABLE 8-17
A random sample of 100 stores from a large chain of 500 garden supply stores was selected to determine the mean number of lawnmowers sold at an end-of-season clearance sale.The sample results indicated a mean of 6 and a standard deviation of 2 lawnmowers sold.A 95% confidence interval (5.623 to 6.377)was established based on these results.
True or False: Referring to Table 8-17,95% of the stores have sold between 5.623 and 6.377 lawnmowers.

Question 13

TABLE 8-17
A random sample of 100 stores from a large chain of 500 garden supply stores was selected to determine the mean number of lawnmowers sold at an end-of-season clearance sale.The sample results indicated a mean of 6 and a standard deviation of 2 lawnmowers sold.A 95% confidence interval (5.623 to 6.377)was established based on these results.
True or False: Referring to Table 8-17,we do not know for sure whether the true population mean is between 5.623 and 6.377 lawnmowers sold.