quote:

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Originally posted by nila

As a marketing analyst for Imperial Products, your task is to determine if a new product is worth marketing nationwide. The director of marketing has stated that at least 85percent of the public must express some desire for the product and, for those who exhibit an interest, the average cost they are willing to pay must be at least $47.50. The director insists that you be 95 percent certain of your findings.

To respond to the director’s request, you survey 50 potential consumers regarding their interest in the product. Thirty-four express an interest in purchasing it. The maximum price each would be willing to pay is shown below. How would you reply to the director’s request for information? Should the product be marketed? How large should the sample be if you want to maintain a 95 percent level of confidence and suffer a maximum error of $2.00 in your estimate of the highest price consumers are willing to pay?


______________________________________

Maximum Prices
______________________________________

47 62 46
43 53 34
54 45 35
65 36 32
54 45 31
34 36 25
38 37 56
35 43 65
43 48 54
37 46 65
54 42 47
63
_______________________________________

Exercise #3

A Keynesian Consumption Function:

In his famous 1936 book, A General Theory of Employment, Interest and Money, the noted British economist John Maynard Keynes proposed a theoretical relationship between income and personal consumption expenditures. Keynes argued that as income went up, consumption would rise by a smaller amount. This theoretical has been empirically tested many times since 1936.

Milton Friedman, former professor of economics at the University of Chicago and winner of the Nobel Prize in economics, collected extensive data on income and consumption in the United States over a long period of time. Shown below are 10 observations on annual levels of consumption and income used by Friedman in his study. Using these data, derive a consumption function under the assumption that there exists a linear relationship between consumption and income. Figures are in billions of dollars.
________________________________________________________________
Year Income Consumption ________________________________________________________________

1 284.8 191.0
2 328.4 206.3
3 345.5 216.7
4 364.6 230.0
5 364.8 236.5
6 398.0 254.4
7 419.2 266.7
8 441.1 281.4
9 447.3 290.1
10 483.7 311.2
_________________________________________________________________

Determine the dependent and independent variable and calculate a consumption factor. Establish the relationship between income and consumption and interpret. Discuss the fit of the data and explain.
Exercise #4

Quality control problem:

According to U.S. News & World Report, a laboratory in Atlanta is processing snake venom for use in medical research. Five processing methods are being tested to determine which is least likely to contaminate the processed venom. If a venom solution is tested as contaminated, it is marked with symbol “2B”. Each method produces 25 vials of venom each day. The vials from each processing method are then boxed for shipment to medical research facilities.
Assume for our purposes that scientists in the laboratory feel that the contamination is uniformly distributed, but others argue that it is not.

Conduct each test and state a conclusion using a significance level of 0.05.


Processing Method Observed

1 34
2 17
3 14
4 12
5 23

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quote:

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Originally posted by nila

As a marketing analyst for Imperial Products, your task is to determine if a new product is worth marketing nationwide. The director of marketing has stated that at least 85percent of the public must express some desire for the product and, for those who exhibit an interest, the average cost they are willing to pay must be at least $47.50. The director insists that you be 95 percent certain of your findings.

To respond to the director’s request, you survey 50 potential consumers regarding their interest in the product. Thirty-four express an interest in purchasing it. The maximum price each would be willing to pay is shown below. How would you reply to the director’s request for information? Should the product be marketed? How large should the sample be if you want to maintain a 95 percent level of confidence and suffer a maximum error of $2.00 in your estimate of the highest price consumers are willing to pay?

______________________________________

Maximum Prices
______________________________________

47		62		46
43		53		34
54		45		35
65		36		32
54		45		31
34		36		25
38		37		56
35		43		65
43		48		54
37		46		65
54		42		47
63
_______________________________________

I fully understand these are three separate questions - probably assigned as an end-of-semester project. So you need show that you deserve the grade you are planning to get.

For the first problem above begin by calculating the mean and the standard deviation.

Then assuming normal distribution calculate the z-score and go from there....

Exercise #3

A Keynesian Consumption Function:

In his famous 1936 book, A General Theory of Employment, Interest and Money, the noted British economist John Maynard Keynes proposed a theoretical relationship between income and personal consumption expenditures. Keynes argued that as income went up, consumption would rise by a smaller amount. This theoretical has been empirically tested many times since 1936.

Milton Friedman, former professor of economics at the University of Chicago and winner of the Nobel Prize in economics, collected extensive data on income and consumption in the United States over a long period of time. Shown below are 10 observations on annual levels of consumption and income used by Friedman in his study. Using these data, derive a consumption function under the assumption that there exists a linear relationship between consumption and income. Figures are in billions of dollars.
________________________________________________________________
Year Income Consumption ________________________________________________________________

1 284.8 191.0
2 328.4 206.3
3 345.5 216.7
4 364.6 230.0
5 364.8 236.5
6 398.0 254.4
7 419.2 266.7
8 441.1 281.4
9 447.3 290.1
10 483.7 311.2
_________________________________________________________________

Determine the dependent and independent variable and calculate a consumption factor. Establish the relationship between income and consumption and interpret. Discuss the fit of the data and explain.
Exercise #4

Quality control problem:

According to U.S. News & World Report, a laboratory in Atlanta is processing snake venom for use in medical research. Five processing methods are being tested to determine which is least likely to contaminate the processed venom. If a venom solution is tested as contaminated, it is marked with symbol “2B”. Each method produces 25 vials of venom each day. The vials from each processing method are then boxed for shipment to medical research facilities.
Assume for our purposes that scientists in the laboratory feel that the contamination is uniformly distributed, but others argue that it is not.

Conduct each test and state a conclusion using a significance level of 0.05.


Processing Method Observed

1 34
2 17
3 14
4 12
5 23

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