"Tongue Piercing May Speed Tooth Loss, Researchers Say" is the headline of an article. The article describes a study of 51 young adults with pierced tongues. The researchers found receding gums, which can lead to tooth loss, in 16 of the participants.

(a) Construct a 95% confidence interval for the proportion of young adults with pierced tongues who have receding gums. (Round your answers to three decimal places.)

( , )

(b) What assumptions must be made for use of the z confidence interval to be appropriate? (Select all that apply.)

1) The sample is voluntary.

2) The sample is a random sample.

3) The sample is independent.

4) The sample size is large.

1. What is the percentage of shared variance between the midterm and final grades in the table below?

   Midterm	Final
   55	100
   60	80
   78	92
   79	95
   80	90
   55	90
   64	40
   89	75
   90	70
   92	82
   94	70
   100	100

   		13%
   		17%
   		25%
   		Less than 1%

A report states that the mean yearly salary offer for students graduating with a degree in accounting is $48,757. Suppose that a random sample of 50 accounting graduates at a large university who received job offers resulted in a mean offer of $49,880 and a standard deviation of $3500. Do the sample data provide strong support for the claim that the mean salary offer for accounting graduates of this university is higher than the national average of $48,757? Test the relevant hypotheses using α = 0.05. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.)

t =

P-value =

Historical delivery times for Jackson Trucking, Inc. have had a mean of 3 hours and a standard deviation of 0.5 hours. A sample of 22 deliveries over the past month provides a sample mean of 3.1 hours and a sample standard deviation of 0.75 hours. Compute 95% confidence interval for the population variance. Select one: A. 0.5770 21.0718 B. 0.3329 21.1487 C. 0.4439 21.5317 D. 0.6663 21.2376

I know the answer is B

(n-1)s2 / x2 mui/2 <= o2 <= (n-1) s2 / X2 1- mui/2

(22-1)0.75sqrt / 35.479 <= o2 <= (22-1)0.75sqrt / 10.283

= 0.3329 <= o2 <= 1.1487

how do you get the 35.479 and 10.283?????

The employee credit union at State University is planning the allocation of funds for the coming year. The credit union makes four types of loans to its members. In addition, the credit union invests in risk-free securities to stabilize income. The various revenue-producing investments together with annual rates of return are as follows:

Type of Loan/Investment Annual Rate of Return (%) Automobile loans 7 Furniture loans 10 Other secured loans 11 Signature loans 12 Risk-free securities 8

The credit union will have $2.3 million available for investment during the coming year. State laws and credit union policies impose the following restrictions on the composition of the loans and investments: • Risk-free securities may not exceed 30% of the total funds available for investment. • Signature loans may not exceed 10% of the funds invested in all loans (automobile, furniture, other secured, and signature loans). • Furniture loans plus other secured loans may not exceed the automobile loans. • Other secured loans plus signature loans may not exceed the funds invested in risk-free securities.

How should the $2.3 million be allocated to each of the loan/investment alternatives to maximize total annual return?

a.Type of Loan/Investment Fund Allocation Automobile loans:

$ Furniture loans

$ Other secured loans

$ Signature loans

$ Risk-free securities

b. What is the projected total annual return?

Annual Return = $

A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8 ounces, the company wants the pack-ages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sample of 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17 ounces. Suppose that in a particular sample of 50 packages, the mean amount dispensed is 8.159 ounces, with a sample standard deviation of 0.051 ounce.

b. Determine the p-value and interpret its meaning.

I am unfamiliar with the excel function that everyone else seems to use for this answer.

2. A sample of 100 is selected from a population with mean µ = 100 and σ = 20.0.

(a) Describe the sampling distribution of the sample mean X¯.

(b) Find P(X >¯ 105).

(c) Find P(100 < X <¯ 105).

(d) Find P(98 < X <¯ 104).

3. According to the U.S. Department of Energy, the average price of unleaded regular gasoline sold at service stations throughout the nation is $1.23 per gallon with a standard deviation of $0.16. A random sample of 45 stations is selected and the pump prices for unleaded gasoline are recorded. Find the probability that the sample mean price:

(a) exceeds $1.28 per gallon,

(b) is less than $1.19 per gallon,

(c) is between $1.20 and $1.27 per gallon,

4. Almost all medical schools in the U. S. require students to take the Medical College Admission Test (MCAT). Suppose that the test scores follow a normal distribution with mean 25.0 and standard deviation 6.5.

(a) One student is selected at random, what is the probability that the student’s score is between 20 and 30?

(b) A random sample of 36 students is selected, what is the probability that their mean score is between 20 and 30?

1. Please provide a detailed description of an original example (i.e., something not discussed in class or the textbook) of a situation in which a paired samples t-test would be most appropriate.

George Caloz & Frères, located in Grenchen, Switzerland, makes prestige high-end custom watches in small lots. One of the company’s products, a platinum diving watch, goes through an etching process. The company has observed etching costs as follows over the last six weeks:

Week	Units			Total Etching Cost
1		14			$	27
2		11			$	20
3		16			$	30
4		10			$	20
5		12			$	25
6		15			$	28
		78			$	150

For planning purposes, management would like to know the amount of variable etching cost per unit and the total fixed etching cost per week.

Required:

1.	Prepare a scattergraph plot. (Place etching costs on the vertical axis and units on the horizontal axis.)

  

Instructions:
1.	On the graph below, use the point tool (Week 1) to plot units on the horizontal axis and total etching cost on the vertical axis.
2.	Repeat the same process for the plotter tools (Week 2 to Week 6).
3.	To enter exact coordinates, click on the point and enter the values of x and y.
4.	To remove a point from the graph, click on the point and select delete option.

      

2(a).

Using the least-squares regression method, estimate the variable and fixed elements of etching cost. (Round your answers to 2 decimal places.)

     

  

2(b).

Express the cost data in (2a) above in the form Y = a + bX. (Round your answers to 2 decimal places.)

     

         

3.	If the company processes thirteen units next week, what would be the expected total etching cost? (Round your intermediate and final answers to 2 decimal places.)

     

Suppose that we are at time zero. Passengers arrive at a train station according to a Poisson process with intensity λ. Compute the expected value of the total waiting time of all passengers who have come to the station in order to catch a train that leaves at time t.

The answer is λt^2/2

A sample of 150 individuals (males and females) was surveyed, and the individuals were asked to indicate their yearly incomes. Their incomes were categorized as follows.

Category 1	$20,000	up to	$40,000
Category 2	$40,000	up to	$60,000
Category 3	$60,000	up to	$80,000

Income Category	Male	Female
Category 1	10	30
Category 2	35	15
Category 3	15	45

We want to determine if yearly income is independent of gender.

a. Compute the test statistic.

b. Using the p-value approach, test to determine if yearly income is independent of gender. Use α = .05. Briefly discuss.

Your leader has asked you to evaluate the defects based on insurance claim type (auto vs. injury). You have a total of 600 claims, with 400 auto, 200 injury, 100 with a defect, and 60 auto or has an injury.

    Provide at least three relevant probabilities for the leader that will be important for use in making business decisions.

    Explain why the selected probabilities are important.

UIT is a computer retail store that sells two kinds of microcomputers: desktops and laptops. The company earns $220 profit on each desktop computer it sells and $500 profit on each laptop. The microcomputers UIT sells are from its wholesaler. This wholesaler can only supply UIT up to 350 desktops and 295 laptops next month. The employees at UIT must spend 30 minutes installing software and checking each desktop computer they sell. The employees spend 50 minutes to complete this process for each of the laptop computers. They expect to have 16000 minutes available from the employees next month. Due to consumers’ demands, the number of desktops cannot be less than the number of laptops. The manager is certain that they can sell all the computer they order, but unsure how many of desktops and laptops they should order to maximize UIT's profit.

(a) Formulate a linear programming model for this problem.

(b) Use the graphical approach to solve the model and report your managerial decision.

(c) Report the total profit for this problem.

(d) The unit profit for a desktop now increases to $450. What will be your revised managerial decision?

(e) Report the revised profit for part (d).

Karin arrives at the post office, which opens at 9:00 a.m., at 9:05 a.m. She finds two cashiers at work, both serving one customer each. The customers started being served at 9:00 and 9:01, respectively. The service times are independent and Exp(8)-distributed. Let Tk be the time from 9:05 until service has been completed for k of the two customers, k = 1, 2. Find ETk for k=1 and 2.

The answer is ET1 =4, ET2 =12.

An automobile manufacturer claims that its van has a 38.4 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 240 vans, they found a mean MPG of 38.1. Assume the standard deviation is known to be 2.0. A level of significance of 0.05 will be used. Find the value of the test statistic. Round your answer to 2 decimal places.

Enter the value of the test statistic.