Question 1: For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.3770. The value of Z is:
Question 2: A worker earns $15 per hour at a plant and is told that only 2.5% of all workers make a higher wage. If the wage is assumed to be normally distributed and the standard deviation of wage rates is $5 per hour, the average wage for the plant is $7.50 per hour.
Question 3: The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. What percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds?
Question 4: If the amount of gasoline purchased per car at a large service station has a population mean of $15 and a population standard deviation of $4 and a random sample of 4 cars is selected, there is approximately a 68.26% chance that the sample mean will be between $13 and $17.
Question 5: The t distribution
- assumes the population is normally distributed.
- approaches the normal distribution as the sample size increases.
- has more area in the tails than does the normal distribution.
- All of the above.
Question 6: A sample of 100 fuses from a very large shipment is found to have 10 that are defective. The 95% confidence interval would indicate that, for this shipment, the proportion of defective fuses is between 0 and 0.28.
Question 7: Suppose we want to test H0 : μ ≥ 30 versus H1 : μ < 30. Which of the following possible sample results based on a sample of size 36 gives the strongest evidence to reject H0 in favor of H1?
Question 8: The larger is the p-value, the more likely one is to reject the null hypothesis.
Question 9: What do we mean when we say that a simple linear regression model is ‘statistically' useful?
- All the statistics computed from the sample make sense.
- The model is an excellent predictor of Y.
- The model is ‘practically' useful for predicting Y.
- The model is a better predictor of Y than the sample mean.
Question 10: Which of the following statements about the method of exponential smoothing is not true?
- It gives greater weight to more recent data.
- It can be used for forecasting.
- It uses all earlier observations in each smoothing calculation.
- It gives greater weight to the earlier observations in the series.
Question 11: A company that manufactures designer jeans is contemplating whether to increase its advertising budget by $1 million for next year. If the expanded advertising campaign is successful, the company expects sales to increase by $1.6 million next year. If the advertising campaign fails, the company expects sales to increase by only $400,000 next year. If the advertising budget is not increased, the company expects sales to increase by $200,000. Identify the outcomes in this decision-making problem.
- Two choices: (1) increase the budget and (2) do not increase the budget.
- Two possibilities: (1) campaign is successful and (2) campaign is not successful.
- Four consequences resulting from the Increase/Do Not Increase and Successful/Not Successful combinations.
- The increase in sales dollars next year.
The data below represents the amount of grams of carbohydrates in a sample serving of breakfast cereal.
10 18 24 30 19 22 24 20 18 25 20 22 19
The coefficient of variation for this data would be Answer %. Answer should be consistent with examples in your Levine et al. text and be between one or two decimal places e.g. 12.3 or 12.34 etc.
Question 12: In a local cellular phone area, company A accounts for 70% of the cellular phone market, while company B accounts for the remaining 30% of the market. Of the cellular calls made with company A, 2% of the calls will have some sort of interference, while 3% of the cellular calls with company B will have interference.
Question 13: Given that a randomly selected cellular call is one that has interference, what is the probability it came from company B?
Answer should be between two and four decimal places e.g. 0.12, 0.123, 0.1234 etc.
The manager of a service station is in the process of analyzing the number of times car owners change the oil in their cars. She believes that the average motorist changes his or her car's oil less frequently than recommended by the owner's manual (two times per year). In a preliminary survey she asked 15 car owners how many times they changed their car's oil in the last 12 months. The results are listed below.
1 1 2 0 3
3 0 1 0 1
2 3 1 3 1
Question 14: The value of the test statistic in this problem is approximately equal to Answer ?
Answer should be between two and four decimal places e.g. 1.23, 1.234, 1.2345 etc.
Question 15: What would be your decision if a hypothesis test was conducted on this problem with the null hypothesis given as H0 : µ ≥ 2 and the alternate hypothesis given as H1 < 2?
- Reject H0 at the 10%, 5% and 1% level of significance.
- Reject H0 at the 10% and 5% level of significance but do not reject H0 at the 1% level of significance.
- Reject H0 at the 10% level of significance but do not reject H0 at the 5% or 1% level of significance.
- Do not reject H0 at either the 10%, 5% or 1% level of significance.
Refer to the following table which contains the sales (in $,000) for a department store for the first ten months of the year.
Month Sales
January 440
February 480
March 590
April 400
May 500
June 550
July 470
August 500
September 600
October 520
Question 16: Using a three period moving average (i.e. MA(3)) as a forecasting method, what is the MAPE for this forecasting model
Question 17: Using simple exponential smoothing (with a smoothing constant of 0.2) as a forecasting method, what is the MAPE for this forecast model Answer %?
The ordered list below resulted from taking a sample of 25 batches of 500 computer chips and determining how many in each batch were defective.
Defects
1, 2, 4, 4, 5, 5, 6, 7, 9, 10, 12, 12, 14, 17, 20, 21, 23, 23, 24, 26, 27, 27, 28, 29, 29
Question 18: If a frequency distribution for the defects data is constructed, using ‘0 but less than 5' as the first class, what would be the relative frequency of the ‘10 but less than 15' class Answer %?
A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is fifty (50) minutes with a standard deviation of forty (40) minutes (the very large standard deviation is due to a variety of factors including a large variation in skills amongst the ‘Do it yourself' home handyman which is traditionally one of the companies customer base). Suppose a random sample of 64 purchasers of this table saw is taken.
Question 19: What is the probability that the sample mean will be less than 46 minutes Answer ?
Question 20: A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. The desired length of the insulation is 12 metres. It is known that the standard deviation in the cutting length is 0.15 metres. A sample of 144 cut sheets yield a mean length of 12.14 metres. This sample will be used to obtain a 90% confidence interval for the mean length cut by machine.
What are the two limits of the confidence interval?
min = Answer
max = Answer
Question 21: An insurance company wishes to examine the relationship between income (in $,000) and the amount of life insurance (in $,000) held by families. The company drew a simple random sample of families and obtained the following results:
Family Income Amount of life insurance
A 40 110
B 80 200
C 110 220
D 80 150
E 80 170
F 120 270
G 60 140
H 100 240
I 60 150
J 90 200
What is the least squares estimate of the slope?
Question 22: What is the least squares estimate of the Y intercept?
Question 23: What is the prediction for the amount of life insurance for a family whose income is $85,000?
Question 24: What would be the residual (error) term for a family income of $90,000?
Question 25: International Pictures is trying to decide how to distribute its new movie 'Claws'. 'Claws' is the story of an animal husbandry experiment at the University of Southern Queensland that goes astray, with tragic results. An effort to breed meatier chickens somehow produces an intelligent, 200 kilogram chicken that escapes from the lab and terrorises the campus. In a surprise ending the chicken is befriended by coach Tim Galvano, who teaches it how to play Rugby and help his team win State, National and World Championships. Because of the movie's controversial nature, it has the potential to be either a smash hit, a modest success, or a total bomb. International is trying to decide whether to release the picture for general distribution initially or to start out with a 'limited first-run release' at a few selected theatres, followed by general distribution after 3 months. The company has estimated the following probabilities and conditional profits for 'Claws':
PROFITS (Millions of $)
Level of success Probability Limited release General distribution
Smash .3 22 12
Modest .4 9 8
Bomb .3 -10 -2
International can run sneak previews of 'Claws' to get a better idea of the movies' ultimate level of success. Preview audiences rate movies as either good or excellent. On the basis of past experiences, it was found that 90% of all smash successes were rated excellent (and 10% rated good), 75% of all modest successes were rated excellent (25% rated good) and 40% of all bombs were rated excellent (60% rated good). The cost of running sneak previews is not cheap. Currently, this stands at $1m.
What is the opportunity loss for a Limited release for a Bomb level of success?
Question 26: What would the optimal action be for International before running the sneak preview?
- Run a limited release with an expected payoff of $7.20m
- Run a limited release with an expected payoff of $6.20m
- Run a general distribution with an expected payoff of $7.20m
- Run a general distribution with an expected payoff of $6.20m
Question 27: What is the maximum amount of money that International would be prepared to pay for an absolutely reliable forecast of the movies' level of success?
Question 28: What would be the joint probability for a ‘bomb success' and excellent preview given that in the past, it was found that 40% of all bomb successes were rated excellent?
Question 29: What is the posterior probability of a bomb given the sneak preview indicates good?
Question 30: The tourist industry is subject to enormous seasonal variation. A hotel in North Queensland has recorded its occupancy rate for each quarter during the past 5 years. These data are shown in the accompanying table.
Table: Occupancy rate
Year
2004 2005 2006 2007 2008
Quarter 1 0.561 0.575 0.594 0.622 0.665
Quarter 2 0.702 0.738 0.738 0.708 0.835
Quarter 3 0.800 0.868 0.729 0.806 0.873
Quarter 4 0.568 0.605 0.600 0.632 0.670
What is the centred moving average that would correspond to Quarter 1 in 2006?
Question 31: What is the adjusted seasonal index for Quarter 1 Answer %?
Question 32: The trend line for this decomposition model can be read off the following partial regression printout (at 3 decimal places) to be Y = 0.650 + 0.004 T where T represents time.
Analysing the partial regression printout, what is the coefficient of determination (R2) for this trend line? (Select the closest correct answer).
- 0.0932 (9.32%)
- 0.3448 (34.48%)
- 0.4545 (45.45%)
- 0.5455 (54.55%)
Question 33: What would be the forecast in Quarter 1, 2009 using the trend line previously given (i.e. Y = 0.650 + 0.004 T) and the relevant adjusted seasonal index?
Question 34: If we exponentially smooth the data in Table 1 with a smoothing constant of 0.1, the smoothed value for Quarter 4 in 2004 would be?
Question 35: If we exponentially smooth the data in Table 1 with a smoothing constant of 0.1, the forecast for Quarter 1 2009 would be?