# STATS Assignment

Question

INSTRUCTIONS:

Read every question carefully. Write your answers and calculations legibly.

Your work must be shown to receive full credit.

Underline your final answer.

Put your name on top of the first problem.

Use three (3) decimal places of accuracy unless instructed otherwise.

Name_____________________

Problem 1 (25 points): The safety director of an insurance company took samples at random from his minor accidents file and classified them according to the time the accident took place.

Number

Time of Accidents

8 – 9 am 6

9 – 10 am 6

10 – 11 am 20

11 – 12 am 8

1 – 2 pm 7

2 – 3 pm 8

3 – 4 pm 19

4 – 5 pm 6

Using the chi-square test and the .01 level of significance, determine whether or not the accidents are evenly distributed throughout the day.

a) What are the Null and Alternate Hypotheses?

b) What is the critical value?

c) What is the Decision Rule?

d) What is the test statistic?

e) What is the decision?

f) What does the decision infer?

Problem 2 (25 points): Bob, a manufacturing plant manager, is inspecting the diameters of ball bearings produced by a suspected malfunctioning unit. He randomly selects a sample of 12 ball bearings and measures the diameters, which are as follows (in millimeters):

Sample 1 152 141 148

Sample 2 150 146 156

Sample 3 155 149 153

Sample 4 156 147 151

a) Construct a Mean Chart. Assume sample sizes of 3. Include the UCL and LCL. Is the process in control? (12.5 points)

b) Construct a Range Chart. Assume sample sizes of 3. Include the UCL and LCL. Is the process in control? (12.5 points)

Problem 3 (25 points): A Los Angeles utility needs to decide whether to invest 5 billion dollars to build a new power plant in 1995. Its current plants produce a total of 5400 Megawatts (MW) of electricity. The actual peak electrical demand of the Los Angeles area since 1980 is shown below.

Actual Peak

Year Demand (MW)

1980 4,069

1981 4,364

1982 4,456

1983 4,445

1984 4,882

1985 4,713

1986 4,742

1987 4,922

1988 4,991

1989 4,774

1990 5,312

1991 5,100

a) What is the Linear Trend equation for this data?

(15 points)

b) Plot the straight line developed from the Linear Trend equation, and the actual Peak demand versus the time, with time being the independent variable. (5 points)

c)What is the projected demand for 1995? (5 points)

Problem 4 (25 points): A manufacturing company has $100,000 available to invest. Doctor Goodbuy, the president and CEO of the company, would like to either expand his production, invest the money in stocks, or purchase a certificate of deposit from the bank. Of course, the unknown is whether the economy will continue at a high level or there will be a recession. He estimates the likelihood of a recession at 20%. Whether there is a recession or not, the certificate of deposit will result in a gain of 6 percent. If there is a recession, he predicts a 10 percent loss if he expands production and a 5 percent loss if he invests in stock. If there is not a recession, an expansion of production will result in a 15 percent gain, and stock investment will produce a 12 percent gain (Use only the amount made or lost in the answers).

1) Develop a payoff table for the various acts and states of nature. (6 points)

2) Compute the total expected payoff for each alternative.

(6 points)

3) Construct an Opportunity Loss Table.(6 points)

4) What is the lowest total expected Opportunity Loss?

(2 points)

5) What decision should Doctor Goodbuy make? (2 points)

6) What is the maximum amount that Doctor Goodbuy should pay to a consultant for financial advise for this scenario (in other words, what is the EVPI?) (3 points)

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