I don’t understand this. Last year [year 1], we decided to drop our highest-end Red model and only produce the Yellow and Green models, because the cost system indicated we were losing money on Red. Now, looking at the preliminary numbers, our profit is actually lower than last year and it looks like Yellow has become a money loser, even though our prices, volumes, and direct costs are the same. Can someone please explain this to me and maybe help me decide what to do next year?

Robert Dolan

President & CEO

Dolan Products

Dolan Products is a small, family-owned audio component manufacturer. Several years ago, the company decided to concentrate on only three models, which were sold under many brand names to electronic retailers and mass-market discount stores. For internal purposes, the company uses the product names Red, Yellow, and Green to refer to the three components.

Data on the three models and selected costs follow:

This year (year 2), the company only produced the Yellow and Green models. Total overhead was $625,400. All other volumes, unit prices, costs, and direct labor usage were the same as in year 1. The product cost system at Dolan Products allocates manufacturing overhead based on direct labor hours.

Required:

a. Compute the product costs and gross margins (revenue less cost of goods sold) for the three products and total gross profit for year 1. (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.)

b. Compute the product costs and gross margins (revenue less cost of goods sold) for the two remaining products and total gross profit for year 2. (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.)
     

c. Should Dolan Products drop Yellow for year 3?   

1. For a particular scenario, we wish to test the hypothesis H₀ : p = 0.48. For a sample of size 50, the sample proportion p̂ is 0.42. Compute the value of the test statistic z_obs. (Express your answer as a decimal rounded to two decimal places.)

2. Which of the following is a valid alternative hypothesis for a one-sided hypothesis test about a population proportion p?

A. p = 0.6

B. p < 0

C. p ≠ 0.7

D. p > 0.3

3. Suppose that the sample proportion p̂ is used to construct a confidence interval for the population proportion p. Assuming that the value of p̂ is fixed, which of the following combinations of confidence levels and sample sizes yield the the widest confidence interval (that is, one with the largest range of values)?

A. 95% confidence level, n = 500

B. 95% confidence level, n = 50

C. 99% confidence level, n = 50

D. 99% confidence level, n = 500

4. Which of the following statements about a confidence interval is NOT true?

A. A confidence interval of size α indicates that there is a probability of α that the parameter of interest falls inside the interval.

B. A confidence interval is generally constructed by taking a point estimate plus or minus the margin of error.

C. A confidence interval is often more informative than a point estimate because it accounts for sampling variability.

D. A confidence interval provides a range of plausible values for a parameter based on the sampling distribution of a point estimator.

5. For a test of H₀ : p = p_{0 vs.} H₁ : p < p₀, the value of the test statistic z _obs is -0.87. What is the p-value of the hypothesis test? (Express your answer as a decimal rounded to three decimal places.)

6. A pilot survey reveals that a certain population proportion p is likely close to 0.37. For a more thorough follow-up survey, it is desired for the margin of error to be no more than 0.03 (with 95% confidence). Assuming that the data from the pilot survey are reliable, what sample size is necessary to achieve this? (Express your answer as an integer, rounded as appropriate.)​​​​​​​

7. Suppose that you are testing whether a coin is fair. The hypotheses for this test are H₀: p = 0.5 and H₁: p ≠ 0.5. Which of the following would be a type II error?

A. Concluding that the coin is not fair when in reality the coin is not fair.

B. Concluding that the coin is fair when in reality the coin is fair.

C. Concluding that the coin is not fair when in reality the coin is fair.

D. Concluding that the coin is fair when in reality the coin is not fair.

1.  50 part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below:

a. Complete the table.

b. What percent of students take exactly one course? _____%

2. The five number summary of a data set was found to be:

0, 4, 11, 15, 20

An observation is considered an outlier if it is below: _____

An observation is considered an outlier if it is above: _____

3.  This data is from a sample. Calculate the mean, standard deviation, and variance.

Please show the following answers to 2 decimal places.

Sample Mean = ______

Sample Standard Deviation = ______

Sample Variance = _____ (Please use the standard deviation above for your calculation.)

Oops - now you discover that the data was actually from a population! So now you must give the population standard deviation.

Population Standard Deviation = _____

4. We are going to calculate the mean, median, and mode for two sets of data. Please show your answer to one decimal place if necessary.

Here is the first data set.

what is the mean (x¯) of this data set? ____

What is the median of this data set? _____

What is the mode of this data set? ____

Here is the second data set.

What is the mean (¯xx¯) of this data set? ____

What is the median of this data set? ____

What is the mode of this data set? _____

5.  E and F are mutually exclusive events. P(E) = 0.91; P(F) = 0.42. Find P(E | F) _____

6.   A special deck of cards has 3 blue cards, and 7 orange cards. The blue cards are numbered 1, 2, and 3. The orange cards are numbered 1, 2, 3, 4, 5, 6 and 7. The cards are well shuffled and you randomly draw one card.

B = card drawn is blue
O = card drawn is odd-numbered

a. How many elements are there in the sample space? _____

b. P(B) =____

7.   The table summarizes results from pedestrian deaths that were caused by automobile accidents.

If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was intoxicated. (Round your answer to 4 decimal places.)
Probability = _______

Provide summary statistics for ?, ?1, ?2. In particular, what is the mean, median, and standard deviation across your 51 observations? Report the results for two simple least-squares regression estimates: ? on ?1 and ? on ?2. For each regression, your report should include the estimate of the intercept, the estimate of the coefficient on the ? variable, as well as the standard error and P-value for each of those estimates. And in words, interpret these results. (How should we interpret the intercepts? What about the slope coefficients? What about the P-values?)  

Case study: Deciding what is effective from different perspectives

The aim of this case study is to illustrate the sometimes competing demands of effectiveness, efficiency and equity. In particular, it should help you to:

Explain what is meant by key terms such as ‘LYG’, ‘QALY’ and ‘ICER’

Use these terms and the information they represent in a decision-making scenario ?        Compare and contrast the demands of effectiveness from different perspectives

Scenario

You are a member of an area prescribing committee (APC) which is reviewing the treatment options for a cancer which is universally rapidly fatal (usually within months) if not treated. For the purposes of this cases study, please assume the following:

There is good evidence supporting the effectiveness of three medicines (A, B and C) in improving health outcomes.

The treatments are mutually exclusive: there is no evidence that patients are better off switching from one to another.

Effectiveness does not depend on patient or disease characteristics.

All costs fall within the first year of treatment.

Costs vary only according to the drug selected, since staff time, etc. are fixed and are the same requirements for each treatment.

The annual budget available for commissioning treatment is US$500,000. ?        The incidence of this cancer in the area covered by your APC is 1,000 new cases each year.

The health economic data are summarized below:

Question 1: Given the available budget of $500,000 per year, how many people could be treated with each option? Please show your calculation and explain briefly about why the current practice is Treatment A. (20%)

Question 2: Measuring the cost-effectiveness by the incremental cost-effectiveness ratio (ICER), compared with the current practice, which treatment (B or C) is more cost-effective for a hospital use? Please show your calculation and explain briefly. (20%)

Question 3: From a patient perspective, which treatment is the most effective by considering the quality of life? Please show your calculation and explain briefly. (20%)

Question 4: From a society perspective, which treatment generates the greatest health gains given the funds available? Please show your calculation and explain briefly. (20%)

Question 5: Which treatment would you recommend to the area prescribing committee (APC): A, B or C? Please discuss your choice from perspectives of equity, efficiency and effectiveness. (20%)

The aim of this case study is to illustrate the sometimes competing demands of effectiveness, efficiency and equity. In particular, it should help you to:

Explain what is meant by key terms such as ‘LYG’, ‘QALY’ and ‘ICER’

Use these terms and the information they represent in a decision-making scenario

Compare and contrast the demands of effectiveness from different perspectives

Scenario You are a member of an area prescribing committee (APC) which is reviewing the treatment options for a cancer which is universally rapidly fatal (usually within months) if not treated. For the purposes of this cases study, please assume the following:

 There is good evidence supporting the effectiveness of three medicines (A, B and C) in improving health outcomes.

 The treatments are mutually exclusive: there is no evidence that patients are better off switching from one to another.

 Effectiveness does not depend on patient or disease characteristics.

 All costs fall within the first year of treatment.

 Costs vary only according to the drug selected, since staff time, etc. are fixed and are the same requirements for each treatment.

 The annual budget available for commissioning treatment is US$500,000.

 The incidence of this cancer in the area covered by your APC is 1,000 new cases each year.

The health economic data are summarized below:

Treatment

A

B

C

Life-Year Gained

A. 0.3

B. 0.6

C. 0.5

Health Utility Index (in each year)

A. 0.8

B. 0.6

C. 0.5

Cost (per patient) A (current practice)

A. $500

B. $1000

C. $800

Question 1: Given the available budget of $500,000 per year, how many people could be treated with each option? Please show your calculation and explain briefly about why the current practice is Treatment A. (20%)

Question 2: Measuring the cost-effectiveness by the incremental cost-effectiveness ratio (ICER), compared with the current practice, which treatment (B or C) is more cost-effective for a hospital use? Please show your calculation and explain briefly. (20%)

Question 3: From a patient perspective, which treatment is the most effective by considering the quality of life? Please show your calculation and explain briefly. (20%)

Question 4: From a society perspective, which treatment generates the greatest health gains given the funds available? Please show your calculation and explain briefly. (20%)

Question 5: Which treatment would you recommend to the area prescribing committee (APC): A, B or C? Please discuss your choice from perspectives of equity, efficiency and effectiveness. (20%)

I Love My Chocolate Company makes dark chocolate and light chocolate. Both products require cocoa and sugar. The following planning information has been made available:

I Love My Chocolate Company does not expect there to be any beginning or ending inventories of cocoa or sugar. At the end of the budget year, I Love My Chocolate Company had the following actual results:

Required:

1. Prepare the following variance analyses for both chocolates and the total, based on the actual results and production levels at the end of the budget year:

     a. Direct materials price variance, direct materials quantity variance, and total variance.

     b. Direct labor rate variance, direct labor time variance, and total variance.

Enter a favorable variance as a negative number using a minus sign and an unfavorable variance as a positive number.

2. The variance analyses should be based on the standard  amounts at actual  volumes. The budget must flex with the volume changes. If the actual  volume is different from the planned volume, as it was in this case, then the budget used for performance evaluation should reflect the change in direct materials and direct labor that will be required for the actual  production. In this way, spending from volume changes can be separated from efficiency and price variances.

I don’t understand this. Last year [year 1], we decided to drop our highest-end Red model and only produce the Yellow and Green models, because the cost system indicated we were losing money on Red. Now, looking at the preliminary numbers, our profit is actually lower than last year and it looks like Yellow has become a money loser, even though our prices, volumes, and direct costs are the same. Can someone please explain this to me and maybe help me decide what to do next year?

Robert Dolan

President & CEO

Dolan Products

Dolan Products is a small, family-owned audio component manufacturer. Several years ago, the company decided to concentrate on only three models, which were sold under many brand names to electronic retailers and mass-market discount stores. For internal purposes, the company uses the product names Red, Yellow, and Green to refer to the three components.

Data on the three models and selected costs follow:

This year (year 2), the company only produced the Yellow and Green models. Total overhead was $764,100. All other volumes, unit prices, costs, and direct labor usage were the same as in year 1. The product cost system at Dolan Products allocates manufacturing overhead based on direct labor hours.

Required:

a. Compute the product costs and gross margins (revenue less cost of goods sold) for the three products and total gross profit for year 1. (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.)

b. Compute the product costs and gross margins (revenue less cost of goods sold) for the two remaining products and total gross profit for year 2. (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.)
     

c. Should Dolan Products drop Yellow for year 3?   

John Fleming, chief administrator for Valley View Hospital, is concerned about the costs for tests in the hospital’s lab. Charges for lab tests are consistently higher at Valley View than at other hospitals and have resulted in many complaints. Also, because of strict regulations on amounts reimbursed for lab tests, payments received from insurance companies and governmental units have not been high enough to cover lab costs.

Mr. Fleming has asked you to evaluate costs in the hospital’s lab for the past month. The following information is available:

1. Two types of tests are performed in the lab—blood tests and smears. During the past month, 1,800 blood tests and 2,400 smears were performed in the lab.
2. Small glass plates are used in both types of tests. During the past month, the hospital purchased 12,000 plates at a cost of $56,400. 1,500 of these plates were unused at the end of the month; no plates were on hand at the beginning of the month.
3. During the past month, 1,150 hours of labor time were recorded in the lab at a cost of $21,850.
4. The lab’s variable overhead cost last month totaled $7,820.

Valley View Hospital has never used standard costs. By searching industry literature, however, you have determined the following nationwide averages for hospital labs:

Plates: Two plates are required per lab test. These plates cost $5.00 each and are disposed of after the test is completed.

Labor: Each blood test should require 0.3 hours to complete, and each smear should require 0.15 hours to complete. The average cost of this lab time is $20 per hour.

Overhead: Overhead cost is based on direct labor-hours. The average rate for variable overhead is $6 per hour.

Required:

1. Compute a materials price variance for the plates purchased last month and a materials quantity variance for the plates used last month.

2. For labor cost in the lab:

a. Compute a labor rate variance and a labor efficiency variance.

b. In most hospitals, one-half of the workers in the lab are senior technicians and one-half are assistants. In an effort to reduce costs, Valley View Hospital employs only one-fourth senior technicians and three-fourths assistants. Would you recommend that this policy be continued?

3-a. Compute the variable overhead rate and efficiency variances.

3-b. Is there any relation between the variable overhead efficiency variance and the labor efficiency variance?

When a surgeon repairs injuries, sutures (stitched knots) are used to hold together and stabilize the injured area. If these knots elongate and loosen through use, the injury may not heal properly because the tissues would not be optimally positioned. Researchers at a university tied a series of different types of knots with two types of suture material, Maxon and Ticron.

Suppose that 112 tissue specimens were available and that for each specimen the type of knot and suture material were randomly assigned. The investigators tested the knots to see how much the loops elongated. The elongations (in mm) were measured and the resulting data are summarized below. For purposes of this exercise, assume it is reasonable to regard the elongation distributions as approximately normal.

(a)

Is there a significant difference in mean elongation between the square knot and the Duncan loop for Maxon thread? (Use α = 0.05. Use a statistical computer package to calculate the P-value.Use μ_{Square Knot} − μ_{Duncan Loop}. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)

t= df = P-value =

(b)

Is there a significant difference in mean elongation between the square knot and the Duncan loop for Ticron thread? (Use α = 0.05. Use a statistical computer package to calculate the P-value.Use μ_{Square Knot} − μ_{Duncan Loop}. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)

t= df = P-value =

(c)

For the Duncan loop knot, is there a significant difference in mean elongation between the Maxon and Ticron threads? (Use α = 0.05. Use a statistical computer package to calculate the P-value.Use μ_Maxon − μ_Ticron. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)

t= df = P-value =