Assignment

 

NOTE TO ALL STUDENTS:

Please print out OR save as htm file on your computer hard drive, as soon as you access it online. Use this copy to prepare your answers. This is because you will NOT be able to save your answers online, and then come back to finalise your assignment at a later date. 

When you have formulated all your answers, then go online again, and insert your answers to each question. 

Only then should you choose the SUBMIT button.

Submission to this assessment will be open one week prior to the due date of 16 May 2011. If you wish to submit prior to this, (that is BEFORE 9 May 2011), you are advised to contact the Course Leader for permission to do so. 

ONLY choose the SUBMIT button when you have fully answered ALL the questions in this assignment. Submission to this assessment will be open one week prior to the due date of 16 May 2011. If you wish to submit prior to this, (that is BEFORE 9 May 2011), you are advised to contact the Course Leader for permission to do so.

REMEMBER: You can ONLY submit this assessment ONCE.

QUESTION 1

True or False: A continuous variable may take on any value within its  http://www.ttc-switch.com/ibm relevant range even though the measurement device may not be precise enough to record it.

 

True

 

False

QUESTION 2

TABLE 2-5 

The following are the durations in minutes of a sample of long-distance phone calls made within the continental United States reported by one long-distance carrier. 

Time (in minutes) Relative

Frequency

0 but less than 5 0.37

5 but less than 10 0.22

10 but less than 15 0.15

15 but less than 20 0.10

20 but less than 25 0.07

25 but less than 30 0.07

30 or more 0.02

 

 

Referring to Table 2-5, if 100 calls were sampled, __________ of them would have lasted less than 5 minutes or at least 30 minutes or more.

 

35

 

37

 

39

 

None of the above.

QUESTION 3

According to the empirical rule, if the data form a ‘bell-shaped’ normal distribution, __________ percent of the observations will be contained within 2 standard deviations around the arithmetic mean.

 

68.26

 

88.89

 

93.75

 

95.44

QUESTION 4

True or False: As a general rule, an observation is considered an extreme value if its Z score is greater than –3.

 

True

 

False

QUESTION 5

If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes.

 

0.3551

 

0.3085

 

0.2674

 

0.1915

QUESTION 6

True or False: The probability that a standard normal random variable, Z, is between 1.00 and 3.00 is 0.1574.

 

True

 

False

QUESTION 7

問題7：雇主的魚市場有一個助理已確定權重的鯰魚通常分布，均值為3.2磅和0.8磅的標準偏差。有多少百分比的4魚樣本的樣本均值在3.0和4.0之間磅？

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?

 

84%

 

67%

 

29%

 

16%

QUESTION 8

True or False: As the sample size increases, the effect of an extreme value on the sample mean becomes smaller.

 

True

 

False

QUESTION 9

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. The 95% confidence interval for the population proportion is 0.59 ± 0.07. Interpret this interval.#p#分頁標題#e#

 

We are 95% confident that the true proportion of all students receiving financial aid is between 0.52 and 0.66.

 

95% of the students get between 52% and 66% of their tuition paid for by financial aid.

 

We are 95% confident that between 52% and 66% of the sampled students receive some sort of financial aid.

 

We are 95% confident that 59% of the students are on some sort of financial aid.

QUESTION 10

True or False: 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.

 

True

 

False

QUESTION 11

How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold:  . Suppose the alternative we wanted to test was H1 : μ < 60. State the correct rejection region for α = 0.05.

 

Reject H0 if t > 1.6604.

 

Reject H0 if t < –1.6604.

 

Reject H0 if t > 1.9842 or Z < –1.9842.

 

Reject H0 if t < –1.9842.

QUESTION 12

True of False: Suppose, in testing a hypothesis about a proportion, the p-value is computed to be 0.043. The null hypothesis should be rejected if the chosen level of significance is 0.05.

 

True

 

False

QUESTION 13

The residuals represent

 

the difference between the actual Y values and the mean of Y.

 

the difference between the actual Y values and the predicted Y values.

 

the square root of the slope.

 

the predicted value of Y for the average X value.

QUESTION 14

The annual multiplicative time-series model does not possess __________ component.

 

a trend

 

a cyclical

 

an irregular

 

a seasonal

QUESTION 15

Blossom’s Flowers purchases roses for sale for Valentine’s Day. The roses are purchased for $10 a dozen and are sold for $20 a dozen. Any roses not sold on Valentine’s Day can be sold for $5 per dozen. The owner will purchase 1 of 3 amounts of roses for Valentine’s Day: 100, 200, or 400 dozen roses. The opportunity loss for buying 200 dozen roses and selling 100 dozen roses at the full price is#p#分頁標題#e#

 

$1,000

 

$500

 

–$500

 

–$2,000

The following information refers to the next question:

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

 

 

QUESTION 16

The standard deviation for this data would be __________ grams.

Answer should be between two and four decimal places e.g. 1.23, 1.234, 1.2345 etc. 

Please do NOT include units (grams) in your answer.

 

 

The following information refers to the next question:

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 17

Given that a randomly selected cellular call is one that has interference, what is the probability it came from company A?

Answer should be between two and four decimal places e.g. 0.12, 0.123, 0.1234 etc. 

Please do NOT include any units in your answer.

 

 

The following information refers to the next two questions:

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 1 2#p#分頁標題#e#

2 0 1 0 1

2 3 1 3 0

 

 

QUESTION 18

The value of the test statistic in this problem is approximately equal to __________?

Answer should be between two and four decimal places e.g. 1.23, 1.234, 1.2345 etc. 

Please do NOT include any units in your answer.

 

 

QUESTION 19

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. 

The following information refers to the next two questions:

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 20

Using a three period moving average (i.e. MA(3)) as a forecasting method, what is the MAD for this forecasting model?

Answer should be between two and four decimal places e.g. 1.23, 1.234, 1.2345 etc. #p#分頁標題#e#

Please do NOT include any units in your answer.

 

 

QUESTION 21

Using simple exponential smoothing (with a smoothing constant of 0.2) as a forecasting method, what is the MAD for this forecast model?

Answer should be between two and four decimal places e.g. 1.23, 1.234, 1.2345 etc. 

Please do NOT include any units in your answer.

 

 

The following information refers to the next question:

The ordered array 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 22

If a frequency distribution for the defects data is constructed, using ‘0 but less than 5’ as the first class, what would be the cumulative relative frequency of the ‘15 but less than 20’ class __________%?

Answer should be a percentage value to whole numbers e.g. 12, 23, 34 etc. 

Please do NOT include units (%) in your answer.

 

 

The following information refers to the next question:

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.#p#分頁標題#e#

QUESTION 23

What is the probability that the sample mean will be less than 44 minutes __________?

Answer should be to four decimal places which is consistent with the number of decimal places listed in your appendix tables e.g. 0.1234 etc. 

Please do NOT include any units in your answer.

 

 

The following information refers to the next question:

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.

QUESTION 24

What are the two limits of the confidence interval __________ and __________?

Answer should be to four decimal places e.g. 1.2345 and 2.3456. 

Please do NOT include any units in your answer.

min =

 

max =

 

The following information refers to the next four questions:

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 60 120

B 80 200

C 100 220

D 80 160

E 90 180

F 120 270

G 110 150

H 100 240

I #p#分頁標題#e#70 160

J 100 210

 

 

QUESTION 25

What is the least squares estimate of the slope? 

Answer should be to four decimal places e.g. 1.2345. 

Please do NOT include any units in your answer.

 

 

QUESTION 26

What is the least squares estimate of the Y intercept? 

Answer should be to four decimal places e.g. 1.2345. 

Please do NOT include any units in your answer.

 

 

QUESTION 27

What is the prediction for the amount of life insurance for a family whose income is $85,000? 

Answer should be to four decimal places and be consistent with your original data set e.g. if your answer was $75,410.90 you would enter 75.4109 as your answer. 

Please do NOT include any units in your answer.

 

 

QUESTION 28

What would be the residual (error) term for a family income of $90,000? 

Answer should be to four decimal places and be consistent with your original data set e.g. if your answer was $940.90 you would enter 0.9409, if your answer was $9,400.90 you would enter 9.4009 etc. 

Please do NOT include any units in your answer.

 

 

The next six questions refer to the following information:

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#p#分頁標題#e# 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.

QUESTION 29

What is the opportunity loss for a Limited release for a Modest level of success? 

Answer should be to whole numbers only. You do not need to put any units in your answer.

 

 

QUESTION 30

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 31

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?

 

$9.6m

 

$7.2m

 

$6.2m

 

$2.4m

QUESTION 32

What would be the joint probability for a ‘modest success’ and excellent preview given that in the past, it was found that 75% of all modest successes were rated excellent? 

Answer should be to two decimal places e.g. 0.12, 0.23, etc. 

Please do NOT include any units in your answer.

 

 

QUESTION 33

What is the posterior probability of a bomb given the sneak preview indicates excellent? #p#分頁標題#e#

Answer should be to four decimal places e.g. 0.1234, 0.2345 etc. 

Please do NOT include any units in your answer.

 

 

QUESTION 34

What is the maximum amount that should be paid for the sneak preview (i.e. what would be the expected value of sample information (EVSI))? Select the closest correct answer.

Use four decimal places in your calculations but you can round off the final answer to 2 decimal places.) 

 

$1.04 million

 

$2.58 million

 

$7.2 million

 

$8.24 million

The next six questions refer to the following information:

(All calculations should be to at least three decimal places)

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 1: 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

 

 

QUESTION 35

What is the centred moving average that would correspond to Quarter 1 in 2006?

Answer should be consistent with the data provided and be to three decimal places e.g. 0.123, 0.456 etc. 

Please do NOT include any units in your answer.

 

 

QUESTION 36

What is the adjusted seasonal index for Quarter 1 __________%?

Answer should be listed to three decimal places in the form 0.123 i.e. 0.123 represents 12.3%, 1.234 represents 123.4% etc. 

Please do NOT include the units (%) in your answer.

 

 

QUESTION 37

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 38

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?

Answer should be consistent with the data provided and be to three decimal places e.g. 0.123, 0.456 etc. 

Please do NOT include any units in your answer.

 

 

QUESTION 39

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?

Answer should be consistent with the data provided and be to three decimal places e.g. 0.123, 0.456 etc. 

Please do NOT include any units in your answer.

 

 

QUESTION 40

If we exponentially smooth the data in Table 1 with a smoothing constant of 0.1, the forecast for Quarter 1 2009 would be?

Answer should be consistent with the data provided and be to three decimal places e.g. 0.123, 0.456 etc. 

Please do NOT include any units in your answer.

 

 

NOTE TO ALL STUDENTS:

ONLY choose the SUBMIT button when you have fully answered ALL the questions in this assignment. 

Students can submit their answers to the CMA assessment any time from one week prior to the due date (i.e. from 3 January 2011) up to and including the stipulated due date of 10 January 2011.

Submission to this assessment will be open one week prior to the due date of 16 May 2011. If you wish to submit prior to this, (that is BEFORE 9 May 2011), you are advised to contact the Course Leader for permission to do so.#p#分頁標題#e#

ONLY choose the SUBMIT button when you have fully answered ALL the questions in this assignment. Submission to this assessment will be open one week prior to the due date of 16 May 2011. If you wish to submit prior to this, (that is BEFORE 9 May 2011), you are advised to contact the Course Leader for permission to do so.

REMEMBER: You can ONLY submit this assessment ONCE.

________________________________________