a) An adviser in student services would like to estimate the average monthly car payment of all IRSC students. From past research, it is known that the standard deviation of the distribution of all IRSC student car payments is $44. Determine the sample size necessary such that the margin of error of the estimate for a 99% confidence interval for the average monthly car payment of all IRSC students is at most $7.23. Round the solution up to the nearest whole number.

n=

b) A public health official in St. Lucie county needs to estimate the average diastolic blood pressure of all residents in St. Lucie county for a report that is being prepared for the Florida Department of Health.

The official randomly selected 142 St. Lucie county residents and found that the mean diastolic blood pressure of the sample was 80 millimeters of mercury (mm Hg).

Using a 98% confidence level, determine the margin of error, EE, and a confidence interval for the mean diastolic blood pressure of all St. Lucie county residents. From past research, it is known that the standard deviation of the distribution of all St. Lucie county residents' diastolic blood pressure is 9 mm Hg.

Report the confidence interval using interval notation. Round solutions to two decimal places, if necessary.

The margin of error is given by E=.

A 98% confidence interval is given by ______

c)

A musicologist is currently writing a report about pop songs in the late 2010s. As a part of her research, the musicologist would like to estimate the mean length of pop songs in the late 2010s. A random sample of 191 pop songs from the 2010s was selected and the average of the sample was found to be 3.14 minutes with a standard deviation of 0.3 minutes.

Find three different confidence intervals - one with a 98% confidence level, one with a 97% confidence level, and one with a 90% confidence level - for the average length of all pop songs in the late 2010s. Notice how the confidence level affects the margin of error and the width of the interval.

Report confidence interval solutions using interval notation. Round solutions to three decimal places, if necessary.

• The margin of error for a 98% confidence interval is given by E=.
  
  A 98% confidence interval is given by .  
  
• The margin of error for a 97% confidence interval is given by E=.
  
  A 97% confidence interval is given by .  
  
• The margin of error for a 90% confidence interval is given by E=.
  
  A 90% confidence interval is given by .  

Ray Archuleta is the chief financial officer for the Feelgood Hospital in San Francisco. Mr. Archuleta 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.

The 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. Prepare the standard costs for direct materials and direct labor lab test. Variable overhead is applied using total standard labor hours at the actual output level.  Use decimals rounded to two places, commas if necessary and no dollar signs.

2. Calculate the six standard cost variances shopwn below for the 4,200 tests completed in the lab last month. Indicate favorable (F) or unfavorable (U). Use whole numbers, no decimals, commas if necessary and no dollar signs.

You may prepare a separate tab in the Budget Problem Worksheet and upload it to show your work.

Factory Overhead Budget
Service Department 1 handles personnel matters. The firm anticipates having 12 factory employees and expects the variable costs to operate the personnel department to average $1,000 per employee. The cost of this department is allocated to other departments on the assumption that there will be three employees in the maintenance department, five employees in the molding department, and four employees in the smoothing department. The personnel department’s fixed
costs are estimated to be $15,000 and will be allocated on a lump sum basis at $3,000 to maintenance, $6,000 to molding and $6,000 to smoothing.
The maintenance department is budgeted to make 100 service calls during the period, 60 calls for the molding department and 40 calls for the smoothing department. The maintenance manager estimates that it will cost an average of $150 in variable costs per service call. The fixed costs of $14,000 are thought to benefit the two production departments equally.
The molding department is expected to incur $29,000 in variable overhead and $42,000 in fixed overhead. The smoothing department is expected to have $32,000 in variable overhead and $8,000 in fixed overhead.
Management has decided to allocated 60% of the fixed overhead cost of molding to XL1 and 40% to XL2 and split the fixed smoothing costs evenly between the two products. Variable costs will be allocated based on direct labor hours.

Direct Labor                     

Molding                                 

XL1: 0.5, XL2: 0.4

Smoothing

XL1: 0.3, XL: 0.2

Std Cost = 15

Personnel Dept

Factory 12 employees

Maintenance 3 employees

Molding 5 employees

Smoothing 4 employees

Variable Cost 1,000 per employee

Fixed Cost 15,000

Maintenance 3,000

Molding 6,000

Smoothing 6,000

Maintenance Dept     

Service Calls 100

Molding 60

Smoothing 40

Variable Cost 150 per service call

Fixed Cost 14,000

Molding 50%

Smoothing 50%

Molding Dept

Variable Cost 29,000

Fixed Cost 42,000

XL1    60%

XL2     40%

Smoothing Dept

Variable Cost 32,000

Fixed Cost 8,000

XL1 50%

XL2 50%

Help Calculate based on above data:

Cost Per direct labor hour

Cost per unit of XL1

Cost per unit of XL2

Fixed Costs charged to production XL1

Cost per unit of XL1

Fixed Costs charged to production of XL2

Cost per Unit of XL2

Flexible Budgeting and Variance Analysis

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.

A scientist wishes to investigate whether exposure to sunlight reduces the amount of time it takes for a particular chemical reaction to take place. There is natural variability in reaction time. Data are recorded for 20 different experiments, 10 instances of reaction time in bright, and 10 instances of reaction time in shade. These are presented in the following table.

The scientist does a statistical test and obtains the output in the following display.

Two sample T-test and Confidence Interval

Two sample T for Bright vs Shade

95% CI for mu Bright – mu Shade: (-1.18,    0.10)

T-Test mu Bright = mu Shade (vs not =): T = -1.78      P = 0.093     DF=18

Both use Pooled StDev = 0.680

The scientist really believes that reactions in bright are on average quicker. But according to the analysis results, it will not be possible to publish anything. The scientist then goes to see a statistician to find out if there is anything that can be done to change the conclusion. The statistician flippantly suggest that a o ne-sided test would do the trick, but emphasises that a better solution by far would involve collecting more data.

1. Explain why a one-sided test will change the conclusion, if a predetermined significance level of 0.05 is chosen

2. Explain the two types of error that may be made when testing. How does the sample size affect the probability of making each one, if a predetermined significance level of 0.05 is chosen?

3. The scientist wants to detect the difference of +/- 0.3 seconds between the mean reaction times. Set the significance level to be 0.05 and the power to be 0.95. It is agreed that more experiments will be run. Do a sample size calculation to determine how many more experiments of each type should be run

Flexible Budgeting and Variance Analysis

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. If there is no variance, enter a zero.

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.

The paint used to make lines on roads must reflect enough light to be clearly visible at night. Let μ denote the true average reflectometer reading for a new type of paint under consideration. A test of H₀: μ = 20 versus H_a: μ > 20 will be based on a random sample of size n from a normal population distribution. What conclusion is appropriate in each of the following situations? (Round your P-values to three decimal places.)

(a)    n = 19, t = 3.3, α = 0.05
P-value =

State the conclusion in the problem context.

Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.     Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

(b)    n = 8, t = 1.7, α = 0.01
P-value =

State the conclusion in the problem context.

Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.     Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

(c)    n = 25,

t = −0.3

P-value =

State the conclusion in the problem context.

Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.     Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

You may need to use the appropriate table in the Appendix of Tables to answer this question.

Miller Toy Company manufactures a plastic swimming pool at its Westwood Plant. The plant has been experiencing problems as shown by its June contribution format income statement below:

*Contains direct materials, direct labor, and variable manufacturing overhead.

Janet Dunn, who has just been appointed general manager of the Westwood Plant, has been given instructions to “get things under control.” Upon reviewing the plant’s income statement, Ms. Dunn has concluded that the major problem lies in the variable cost of goods sold. She has been provided with the following standard cost per swimming pool:

*Based on machine-hours.

During June the plant produced 7,000 pools and incurred the following costs:

1. Purchased 29,500 pounds of materials at a cost of $2.55 per pound.

2. Used 24,300 pounds of materials in production. (Finished goods and work in process inventories are insignificant and can be ignored.)

3. Worked 3,400 direct labor-hours at a cost of $7.30 per hour.

4. Incurred variable manufacturing overhead cost totaling $8,400 for the month. A total of 2,400 machine-hours was recorded.

It is the company’s policy to close all variances to cost of goods sold on a monthly basis.

Required:

1. Compute the following variances for June:

a. Materials price and quantity variances.

b. Labor rate and efficiency variances.

c. Variable overhead rate and efficiency variances.

2. Summarize the variances that you computed in (1) above by showing the net overall favorable or unfavorable variance for the month.

A company which manufactures compact discs has found that demand for its product has been increasing rapidly over the last 12 months. A decision now has to be made as to how production capacity can be expanded to meet this demand. Three alternatives are available: (i) Expand the existing plant; (ii) Build a new plant in an industrial development area; (iii) Subcontract the extra work to another manufacturer. The returns which would be generated by each alternative over the next 5 years have been estimated using three possible scenarios: (i) Demand rising at a faster rate than the current rate; (ii) Demand continuing to rise at the current rate; (iii) Demand increasing at a slower rate or falling. These estimated returns, which are expressed in terms of net present value, are shown below (net present values in $000s): Scenario Course of action Demand rising faster Demand rising at current rate Demand increasing slowly or is falling Expand 500 400 ?150 Build new plant 700 200 ?300 Subcontract 200 150 ?50 Exercises 239 (a) The company’s marketing manager estimates that there is a 60% chance that demand will rise faster than the current rate, a 30% chance that it will continue to rise at the current rate and a 10% chance that it will increase at a slower rate or fall. Assuming that the company’s objective is to maximize expected net present value, determine (i) The course of action which it should take; (ii) The expected value of perfect information. (b) Before the decision is made, the results of a long-term forecast become available. These suggest that demand will continue to rise at the present rate. Estimates of the reliability of this forecast are given below: p(forecast predicts demand increasing at current rate when actual demand will rise at a faster rate) = 0.3 p(forecast predicts demand increasing at current rate when actual demand will continue to rise at the current rate) = 0.7 p(forecast predicts demand increasing at current rate when actual demand will rise at a slower rate or fall) = 0.4 Determine whether the company should, in the light of the forecast, change from the decision you advised in (a). (c) Discuss the limitations of the analysis you have applied above and suggest ways in which these limitations could be overcome.

You are testing a treatment for a new virus. Effectiveness is judged by the percent reduction in symptoms after two weeks.It is known that if left untreated, symptoms will reduce on their own by 0.185 (18.5%) with a standard deviation of 0.123. Three trials were run simultaneously.Trial 1 involved giving the participants a sugar pill. Patients in Trial 2 were given Agent A. Patients in Trial 3 were given Agent B. Results showing the amount of symptom reduction for the various trials are summarized in the table to the left. Note that this is NOT a paired t-test.Patient 1 just means the first patient to be given the treatment in each trial. Patient 1 is a different person in each trial.

1) At the 80%, 90% and 95% confidence levels (alpha = 0.2, 0.1 and 0.05) compare Agent A, Agent B and the Sugar Pill results to the population symptom reduction. Use a one-tail hypothesis test.