1)  A light bulb producing company states that its lights will last an average of 1200 hours with a standard deviation of 200 hours.  A sample of 100 light bulbs from the company were tested and the researcher found that the average life of each light bulb was 1050 hours.  At a 95% confidence level, determine whether these light bulbs are in compliance with the company’s claim.

2)  A company’s human resource department claims that all employees are present on the average 4 days out of the work week with a standard deviation of 1.  They hired an outside company to do an audit of their employees’ absences.  The company took a sample a 10 people and found that on the average the employees were present 3 days per week.  With a 95% confidence level, determine whether the company’s claim is true based on the data from the sample.

3)  A teacher claims that all of her students pass the state mandated test with an average of 90 with a standard deviation of  10.  The principal gave the test to 20 of her students to see if the teacher’s claim was true.  He found that the average score was 75.  With a 95% confidence level, determine whether the teacher is making the correct claim about all of her students.

4)  The lifeguard’s at a local pool have to be able to respond to a distressed swimmer at an average of 10 seconds with a standard deviation of 4 in order to be considered for employment.  If a sample of 100 lifeguards showed that their average response time is 15 seconds, with a confidence level of 95% determine whether this group may be considered for employment.

5)  It is believed that an average of  20 mg of iodine is in each antibiotic cream produced by a certain company with a standard deviation of 5 mg.  The company pulled 150 of its antibiotic creams and found that on the average each cream contained 29 mg of iodine.  Determine with a 95% confidence level whether or not these creams are in compliance with the company’s belief?

For questions 6 – 10 use the chi-squared distribution to test the hypothesis.

6)  A restaurant owner wants to see if the business is good enough for him to purchase a restaurant.  He asks the present owner for a breakdown of how many customers that come in for lunch each day and the results are as follows:  Monday – 20, Tuesday – 30, Wednesday – 25, Thursday – 40 and Friday – 55.  The prospective owner observes the restaurant and finds the following number of customers coming for lunch each day:  Monday- 30, Tuesday – 15, Wednesday- 7, Thursday 40, and Friday – 33.  At a 95% confidence level determine whether the present owner reported the correct number of customers for lunch each day.

7)  An employer polled its employers to see if they agree with the proposed new store hours and whether or not their present shift made a difference in their answers.  The customers answered 1 for agree, 2 for don’t know, and 3 for disagree.  Nine first shift employees answered “agree”, 15 second shift employees answered “agree”, and 20 third shift employees answered agree.  With a 95% confidence level determine whether or not the employees’ present shift played a role in their responses to the poll.

8)  A politician surveyed 100 citizens to determine if their job title had anything to do with the way they responded to the following statement:  “A city-wide curfew will be put into place.  Select the time that you think it should be put into place.  8pm, 9pm, or 10pm”.  He is mostly concerned with the 10 pm responses.  25 teachers chose 10pm, 40 doctors chose 10pm, and 35 police responded 10pm.  With a 95% confidence level, determine whether job title plays a role in how the citizens responded to the statement.

9)  A meter reader did an experiment to see if there is a relationship between the number of tickets she writes and the number of blocks she is away from the park that is considered the heart of the city.  At 0 blocks from the park she writes 35 tickets, at 1 block away from the park she writes 25 tickets, at 2 blocks from the park she writes 20 tickets and at 3 blocks from the park she writes 25 tickets.  Use a 95% confidence level.

10)  A high school principal asks his students to respond to the following statement:  “School should start at 9:00am rather than 7:00am.  Answer 1 for agree, 2 for don’t know, and 3 for disagree.”  There were 90 seniors who answered agree, 35 juniors, 30 sophomores, and 25 freshmen.  Help the principal decide with a 95% confidence level that the students’ status played a role in how they responded to the question.

You are a statistician working for a drug company. A few new scientists have been hired by your company. They are experts in pharmacology, but are not experts in doing statistical studies, so you will explain to them how statistical studies are done when testing two samples for the effectiveness of a new drug. The two samples can be dependent or independent, and you will explain the difference.

Concept being Studied

Your focus is on hypothesis tests and confidence intervals for two populations using two samples, some of which are independent and some of which are dependent. These concepts are an extension of hypothesis testing and confidence intervals which use statistics from one sample to make conclusions about population parameters.

What to Submit

To complete this assignment, you must first download the worksheet and then complete it.

You will also develop a PowerPoint presentation for the newly hired scientists on these topics, and you have been asked to provide two real-life examples that you will describe step-by-step. Your boss has asked you to include the following slides:

Slide 1: Title slide

Slide 2: Describes the two differences between independent and dependent samples

Slide 3: Provides an example of independent samples when testing a new drug

Slide 4: Shows how to set up a hypothesis test for two independent proportions: One to test whether they are equal and another one to test whether one proportion is larger than the other

Slide 5: Shows the formula for the test statistic for two independent proportions and lists what each variable in the formula represents

Slide 6: Shows the formula for the margin of error (E) when doing a confidence interval on two proportions and explains what each variable stands for

Slide 7: Other than proportions, describes what other types of hypothesis tests can be done for two independent samples

Slide 8: Provides an example of dependent samples (also known as matched pairs) when testing a new drug. The two samples should be a before and after test with the same group

Slide 9: Shows the t formula for the test statistic for matched pairs and explains what each variable represents

Slide 10: Show what a confidence interval for matched pairs would look like using only variables. Also, include the formula for the Margin of Error and state what each variable represents

To show the formulas above, you may need to use the following variables which you can copy from here:

x̅, p̂, q̂, p̅, q̅, d̅, ∑, μ, σ, σ2, α

QUESTION 1

1.Choose the one alternative that best completes the statement or answers the question. Solve the problem. Round dollar amounts to the nearest dollar.

Find the yearly straight-line depreciation of a home theatre system including the receiver, main audio speakers, surround sound speakers, audio and video cables, and blue-ray player that costs $3100 and has a salvage value of $900 after an expected life of 5 years in a hotel lobby.

$900

$180

$440

$620

10 points   

QUESTION 2

1.Solve the problem. Round unit depreciation to nearest cent when making the schedule, and round final results to the nearest cent.

A barge is expected to be operational for 280,000 miles. If the boat costs $19,000.00 and has a projected salvage value of $1900.00, find the unit depreciation.

$0.06

$0.60

$0.70

$0.07 

10 points   

QUESTION 3

1.Solve the problem. Round unit depreciation to nearest cent when making the schedule, and round final results to the nearest cent.

A construction company purchased a piece of equipment for $1520. The expected life is 9000 hours, after which it will have a salvage value of $380. Find the amount of depreciation for the first year if the piece of equipment was used for 1800 hours. Use the units-of-production method of depreciation.

$177.33

$136.50

$304.00

$228.00

10 points   

QUESTION 4

1.Solve the problem using the information given in the table and the weighted-average inventory method. Round to the nearest cent.

Calculate the average unit cost.

Date of PurchaseUnits PurchasedCost Per Unit

Beginning Inventory25$32.12

March 170$25.24

June 165$36.24

August 140$20.81

$32.90

$143.95

$28.79

$24.77 

10 points   

QUESTION 5

1.Solve the problem using the information given in the table and the weighted-average inventory method. Round to the nearest cent.

Calculate the cost of ending inventory.

Date of PurchaseUnits PurchasedCost Per Unit

Beginning Inventory25$33.18

March 170$28.60

June 165$38.75

August 140$21.49

Units Sold68 

$1461.32

$3116.05

$4298.00

$4098.50

10 points   

QUESTION 6

1.Solve the problem using the information given in the table and the weighted-average inventory method. Round to the nearest cent.

Calculate the cost of goods sold.

Date of PurchaseUnits PurchasedCost Per Unit

Beginning Inventory25$34.13

March 170$27.34

June 165$35.61

August 140$20.77

Units Sold62 

$4079.63

$1832.87

$9992.13

$5912.50

10 points   

QUESTION 7

1.Solve the problem. Use a fraction for the rate and round dollar amounts to the nearest cent.

Jeremy James is depreciating solar panels purchased for $3600. The scrap value is estimated to be $900. He will use double-declining-balance and depreciate over 6 years. What is the first year’s depreciation?

$1200.00

$450.00

$600.00 

$900.00 

10 points   

QUESTION 8

1.Solve the problem. Use a fraction for the rate and round dollar amounts to the nearest cent.

Eric Johnson is depreciating a kitchen oven range purchased for $1720. The scrap value is estimated to be $172. He will use double-declining-balance and depreciate over 30 years. What is the first year’s depreciation?

$57.33

$103.20 

$51.60 

$114.67 

10 points   

QUESTION 9

1.Solve the problem. Use a fraction for the rate and round dollar amounts to the nearest cent.

Jane Frankis is depreciating a train engine purchased for $86,000. The scrap value is estimated to be $5000. She will use double-declining-balance and depreciate over 40 years. What is the first year’s depreciation?

$2025.00

$4050.00 

$4300.00 

$2150.00 

10 points   

QUESTION 10

1.Find the depreciation for the indicated year using MACRS cost-recovery rates for the properties placed in service at midyear. Round dollar amounts to the nearest cent.

Property ClassDepreciation YearCost of Property

3-year3$86,600.00

$28,863.78

Individual Assignment – Regression Case

The risk manager for Big Mac is undertaking a comprehensive analysis of the workers’ compensation injury claims for the firm’s U.S. operations. She has collected monthly data over the last three years with regard to workers’ compensation claims and several other items that she feels may be helpful in predicting future claims.

You are a consultant with a risk management consulting firm specializing in detailed quantitative analysis of problems facing corporate risk managers. Your firm has been retained by Big Mac to perform a comprehensive regression analysis of its workers’ compensation claims.

The data provided to you by Big Mac consists of the following information stored in the file data.XLS.

Variable Name Description of Variable

CLAIMS The number of workers’ compensation injury claims.

MALE The proportion of the work force that is male.

SAFETY The dollar amount of expenditures on safety programs in thousands.

SALES The dollar amount of gross sales in millions.

PARTTM The proportion of the work force that is part-time.

EMPLOYS The number of employees in thousands.

Before you start, please make sure you understand the underlying analytical techniques that you are using (regression analysis). In your written report, please address all of the following points and/or recommendations to the risk manager at Big Mac:

1. Before looking at the data, please use intuition to describe each variable’s probable predictive power and direction of relationship with CLAIMS.

2. Calculate and analyze the correlation matrix. Explain some of the more significant correlations between the independent variables and CLAIMS, as well as between the independent variables themselves. Please make sure to include in your report the correlation

table you obtain from Excel.

3. Perform a comprehensive regression analysis for CLAIMS. This includes calculation and analysis of coefficients, p-values (or t-values), coefficients of determination (R2), etc. Please make sure to include in your report the regression output from Excel including the following: Regression Statistics including R Square, Adjusted R Square, Standard Errors; as well as coefficient, standard error, p-value and t stat for all explanatory/independent variables.

4. Identify and describe the model (i.e., which independent variables should be included – a hint here, not all variables are necessarily needed, pending on statistical significance) that you feel best predicts CLAIMS. Justify the selection of this model from both conceptual and statistical viewpoints. This includes a statement of the identified model that a “non-statistician” could understand.

5. Is there an alternative model that is almost as good as your first choice as identified in your answer to number 4? If so, describe it.

6. State several managerial recommendations that you would make based on the model identified in number 4.