1.) The method of tree ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution.

(a) Use a calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviation s. (Round your answers to the nearest whole number.)

(b) Find a 90% confidence interval for the mean of all tree ring dates from this archaeological site. (Round your answers to the nearest whole number.)

2.) How much does a sleeping bag cost? Let's say you want a sleeping bag that should keep you warm in temperatures from 20°F to 45°F. A random sample of prices ($) for sleeping bags in this temperature range is given below. Assume that the population of x values has an approximately normal distribution.

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean price x and sample standard deviation s. (Round your answers to two decimal places.)

(b) Using the given data as representative of the population of prices of all summer sleeping bags, find a 90% confidence interval for the mean price μ of all summer sleeping bags. (Round your answers to two decimal places.)

3.) How much do wild mountain lions weigh? Adult wild mountain lions (18 months or older) captured and released for the first time in the San Andres Mountains gave the following weights (pounds):

Assume that the population of x values has an approximately normal distribution.

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean weight x and sample standard deviation s. (Round your answers to one decimal place.)

(b) Find a 75% confidence interval for the population average weight μ of all adult mountain lions in the specified region. (Round your answers to one decimal place.)

Part 2:

1. You are investigating the electrical testing circuits and find that, in an inductive circuit, the relationship between instantaneous current i (amps) and the time t (secs) is given by:

i = 2.1(1-e^-9t)

You have been asked to determine the time taken for the current to rise from 1 to 1.5 amps.

Comment on the time taken for the current to rise the same increment from 1.5 to 2 amps and give reasons. You are not required to evaluate this.

2. The drive system of a conveyor used to transport the engine parts is made up of an open belt which passes over two pulleys. The pulleys have diameters of 200mm and 320mm respectively and the distance between centres is 600 mm.

You have been asked to determine the length of the belt, using trigonometric techniques, assuming the belt is in tension.

3. An electrical cable is to be suspended across two machines. The machines are a distance of 4.5 metres apart. The cable takes the shape of a catenary of the form y = c cosh (x/ where x is the horizontal distance of any given point on the catenary from its centre and y is it’s height from the ground surface. You have been asked to determine the fixing point height (y) if the minimum clearance (c) is to be 3m at the centre of the catenary.

1. During a 10-year period, the standard deviation of annual returns on a portfolio you are analyzing was 15 percent a year. You want to see whether this record is sufficient evidence to support the conclusion that the portfolio’s underling variance of return was less than 400, the return variance of the portfolio’s benchmark.

1. Formulate null and alternative hypotheses consistent with the verbal description of or objective.

2. Identify the test statistics for conducting a test of the hypothesis in part A

3. Identify the rejection point or point at the 0.05 significance level for the hypothesis tested in Part A

4. Determine whether the null hypothesis is rejected or not rejected at the 0.05 level of significance.

please show work

Suppose

140

geology students measure the mass of an ore sample. Due to human error and limitations in the reliability of the​ balance, not all the readings are equal. The results are found to closely approximate a normal​ curve, with mean

83

g and standard deviation

3

g. Use the symmetry of the normal curve and the empirical rule as needed to estimate the number of students reporting readings between

80

g and

86

g.

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Question: A physician wants to know if the number of male esophageal cancer patients diagnosed with multipl...

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A physician wants to know if the number of male esophageal cancer patients diagnosed with multiple primary tumors differs from the proportion of female esophageal cancer patients with the same diagnosis. She selects random samples of 60 male and 40 female esophageal cancer patients and records the number in each sample diagnosed with multiple primary tumors. 40 men and 10 women with multiple primary tumors are identified.

What is the null hypothesis for this study?

If the tabulated critical value of the chi-square statistic for the 5% level of significance is 3.84, what is the most appropriate conclusion that can be drawn from this study?

The proportion of male esophageal cancer patients diagnosed with multiple primary tumors differs from the proportion of female esophageal cancer patients diagnosed with such tumors (p<0.05).

The proportion of male esophageal cancer patients diagnosed with multiple primary tumors does not differ from the proportion of female esophageal cancer patients diagnosed with such tumors (p>0.05).

It is 95% certain that the proportion of male esophageal cancer patients diagnosed with multiple primary tumors equals the proportion of female esophageal cancer patients diagnosed with such tumors.

The investigator can be 95% certain that more men than women have esophageal cancer.

Which of the following statements is an accurate interpretation of the p-value associated with the study conclusion?

The observed difference in sample frequencies is likely to be due to random chance.

The probability of obtaining the given sample results by random chance is less than 5%.

The sample sizes are too small to detect a significant difference in frequency.

The investigator can be certain that the proportion of men diagnosed with multiple primary tumors differs from the proportion of women with the same diagnosis.

The proportion of male esophageal cancer patients with multiple primary tumors is greater than that of female esophageal cancer patients with such tumors.

An association exists between gender and the presence of multiple primary tumors.

The proportion of men with esophageal cancer differs from that of women esophageal cancer.

The proportion of male esophageal cancer patients diagnosed with multiple primary tumors does not differ from that of female esophageal cancer patients diagnosed with multiple primary tumors.

The calculated value of the test statistic is:

0.65

16.67

14.04

0.72

question 23

Given a data with y as a response variable and x1,x2, and x3 as explanatory variable, a regression equation relates y to x1 and another relates y to x1,x2, and x3. Calculate the first degree of freedom df1 for testing

H0:β2=β3=0,HA:β2≠0orβ3≠0.

A. 1

B. 2

C. 3

D. 4

question 25

The following table shows the output of a regression model to explain SAT math scores.

Can we conclude that there is a statistically significant gender difference in math scores at the 5% level ?

A. Yes

B. No

question 26

The following regression output is obtained from estimating

y=β0+β1x+β2d+β3xd+ϵ

where d is a dummy variable.

Is there a significant interaction effect between x and d at 5% significance level?

A. Yes

B. No

question 27

Consider the following estimated regression equation

Salary=55.8+3.6∗(Age)−0.7∗(Gender)

where Gender is a dummy variable that takes 0 for a male and 1 for a female.

Compute the predicted salary for a 43 year old woman.

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. In a marketing survey, a random sample of 996 supermarket shoppers revealed that 272 always stock up on an item when they find that item at a real bargain price. (a) Let p represent the proportion of all supermarket shoppers who always stock up on an item when they find a real bargain. Find a point estimate for p. (Round your answer to four decimal places.) 0.273 Incorrect: Your answer is incorrect. (b) Find a 95% confidence interval for p. (Round your answers to three decimal places.) lower limit 0.273 Incorrect: Your answer is incorrect. upper limit 0.028 Incorrect: Your answer is incorrect. Give a brief explanation of the meaning of the interval. 95% of all confidence intervals would include the true proportion of shoppers who stock up on bargains. 95% of the confidence intervals created using this method would include the true proportion of shoppers who stock up on bargains. 5% of all confidence intervals would include the true proportion of shoppers who stock up on bargains. 5% of the confidence intervals created using this method would include the true proportion of shoppers who stock up on bargains. Incorrect: Your answer is incorrect. (c) As a news writer, how would you report the survey results on the percentage of supermarket shoppers who stock up on items when they find the item is a real bargain? Report the confidence interval. Report p̂ along with the margin of error. Report the margin of error. Report p̂. Incorrect: Your answer is incorrect. What is the margin of error based on a 95% confidence interval? (Round your answer to three decimal places.)

1. The following probability distribution represents the number of people living in a Household (X), and the probability of occurrence (P(X)). Compute the Expected Value (mean), the Variance and the Standard Deviation for this random variable. Show Your Calculations for the Mean.

    X      1         2        3          4        5               

P(X)    .30     .33      .24        .08       .05     

2. Use the binomial formula to compute the probability of a student getting 7 correct answers on a 10 question Quiz, if the probability of answering any one question correctly is 0.84. SHOW YOUR WORK.

3. Submit your answers to the following binomial questions. You may use the appendix table B #5 to answer parts (a) and (b). According to a government study, 15% of all children live in a household that has an income below the poverty level. If a random sample of 15 children is selected:

a) what is the probability that 5 or more live in poverty?

b) what is the probability that 5 live in poverty?

c) what is the expected number (mean) that live in poverty? What is the variance? What is the standard deviation?

1. a good rule of thumb when presenting data with a graph is to

a. label all items

b. make sure your graph communicates only one idea

c. limit the number of words

d. all of the above

2. in a normal distribution with a mean of 100 and a standard deviation of 15. what is the probability that a score will be 85 or lower?

3. which of the following sets of scores has the least variability?

a. 7,10,11,15,19

b. 7,7,8,8,10,11

c. 6,6,7,7,7,7

d. 7,7,7,7,7,7

4. which of the following correlations would be interpreted as a very weak relationship?

a. -0.35

b. -0.83

c. 0.15

d. 0.75

5. In the following data set, what is the mode? Dataset (n=5): 6,4,1,3,6

a. 3

b. 6

c. 4

d. 1

6. in a well-designed study, it is possible to generalize your results from the study sample to population

T/F

7. All statistically significant results are meaningful

T/F

8. in the field of health administration, statistics is used for:

a.conducting research

b. guiding policy changes

c. measuring performance

d. all of the above

Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments: A, B, and C. The labor-hour requirements, by department, are as follows:

During the next production period, the labor-hours available are 490 in department A, 390 in department B, and 90 in department C. The profit contributions per unit are $29 for product 1, $32 for product 2, and $34 for product 3. Use a software package LINGO.

1. Formulate a linear programming model for maximizing total profit contribution. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) If constant is “1”, it must be entered in the box.
   
   Let P_i = units of product i produced
   

   Max	______P1	+	______P2	+	______P3
   s.t.
   	______P1	+	______P2	+	______P3	≤	______
   	______P1	+	______P2	+	______P3	≤	______
   	______P1	+	______P2	+	______P3	≤	______
   P1, P2, P3 ≥ 0

2. Solve the linear program formulated in part (a). How much of each product should be produced, and what is the projected total profit contribution?
   
   P₁ = ______
   P₂ = ______
   P₃ = ______
   
   Profit = $  ______
3. After evaluating the solution obtained in part (b), one of the production supervisors noted that production setup costs had not been taken into account. She noted that setup costs are $440 for product 1, $590 for product 2, and $640 for product 3. If the solution developed in part (b) is to be used, what is the total profit contribution after taking into account the setup costs?
   
   Profit = $  ______
4. Management realized that the optimal product mix, taking setup costs into account, might be different from the one recommended in part (b). Formulate a mixed-integer linear program that takes setup costs into account. Management also stated that we should not consider making more than 195 units of product 1, 170 units of product 2, or 160 units of product 3. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) If constant is “1”, it must be entered in the box. Enter “0” if your answer is zero.
   
   Here introduce a 0-1 variable y_i that is one if any quantity of product i is produced and zero otherwise.
   

   Max

   ______P1

   +

   ______P2

   +

   ______P3

   +

   ______y1

   +

   ______y2

   +

   ______y3

   s.t.

   ______P1

   +

   ______P2

   +

   ______P3

   ≤

   ______

   ______P1

   +

   ______P2

   +

   ______P3

   ≤

   ______

   ______P1

   +

   ______P2

   +

   ______P3

   ≤

   ______

   ______P1

   +

   ______y1

   ≤

   ______

   ______P2

   +

   ______y2

   ≤

   ______

   ______P3

   +

   ______y3

   ≤

   ______

   P1, P2, P3 ≥ 0; y1, y2, y3 = 0, 1

5. Solve the mixed-integer linear program formulated in part (d). How much of each product should be produced, and what is the projected total profit contribution? Compare this profit contribution to that obtained in part (c). Enter “0” if your answer is zero.
   
   P₁ = ______
   P₂ = ______
   P₃ = ______
   
   Profit = $  ______
   
   The profit is increased by $ ______.

Please fill out all the blanks! Thank you!!

Let x be the average number of employees in a group health insurance plan, and let y be the average administrative cost as a percentage of claims.

x 3 7 15 39 73

y 40 35 30 25 20

(a) Make a scatter diagram of the data and visualize the line you think best fits the data.

(b) Would you say the correlation is low, moderate, or strong? positive or negative?pLEASE SELECT CORRECT ANSWER

moderate and positive

low and negative

moderate and negative

low and positive

strong and positive

strong and negative

(c) Use a calculator to verify that Σx = 137, Σx2 = 7133, Σy = 150, Σy2 = 4750, and Σxy = 3250. Compute r. (Round your answer to three decimal places.) r =

As x increases, does the value of r imply that y should tend to increase or decrease? Explain. SELECT CORRECT ANSWER

Given our value of r, y should tend to decrease as x increases.

Given our value of r, y should tend to increase as x increases.

Given our value of r, y should tend to remain constant as x increases.

Given our value of r, we cannot draw any conclusions for the behavior of y as x increases.

A multinational firm wants to estimate the average number of hours in a month that their employees spend on social media while on the job. A random sample of 83 employees showed that they spent an average of 21.5 hours per month on social media, with a standard deviation of 2.5. Construct and interpret a 95% confidence interval for the population mean hours spent on social media per month.

Exercises for Probability

Exercise 2-17

Evertight, a leading manufacturer of quality nails, produces 1-, 2-, 3-, 4-, and 5-inch nails for various uses. In the production process, if there is an over- run or the nails are slightly defective, they are placed in a common bin. Yesterday, 651 of the 1-inch nails, 243 of the 2-inch nails, 41 of the 3-inch nails, 451 of the 4-inch nails, and 333 of the 5-inch nails were placed in the bin.

1. What is the probability of reaching into the bin and getting a 4-inch nail?
2. What is the probability of getting a 5-inch nail?
3. If a particular application requires a nail that is 3 inches or shorter, what is the probability of getting a nail that will satisfy the requirements of the application?

Exercise 2-18

Last year, at Northern Manufacturing Company, 200 people had colds during the year. One hundred fifty- five people who did no exercising had colds, and the remainder of the people with colds were involved in a weekly exercise program.  Half of the 1,000 employees were involved in some type of exercise.

1. What is the probability that an employee will have a cold next year?
2. Given that an employee is involved in an exercise program, what is the probability that he or she will get a cold next year?
3. What is the probability that an employee who is not involved in an exercise program will get a cold next year?
4. Are exercising and getting a cold independent events? Explain your answer.

Exercise 2-27

In a sample of 1,000 representing a survey from the entire population, 650 people were from Laketown, and the rest of the people were from River City. Out of the sample, 19 people had some form of cancer.  Thirteen of these people were from Laketown.

1. Are the events of living in Laketown and having some sort of cancer independent?
2. Which city would you prefer to live in, assuming that your main objective was to avoid having cancer?

Exercise 1

An engineering company advertises a job in three papers, A, B and C. It is known that these papers attract undergraduate engineering readerships in the proportions 2:3:1. The probabilities that an engineering undergraduate sees and replies to the job advertisement in these papers are 0.002, 0.001 and 0.005 respectively. Assume that the undergraduate sees only one job advertisement.

1. If the engineering company receives only one reply to it advertisements, calculate the probability that the applicant has seen the job advertised in place A.
2. If the company receives two replies, what is the probability that both applicants saw the job advertised in paper A?

Exercise 2-33

Gary Schwartz is the top salesman for his company.  Records indicate that he makes a sale on 70% of his sales calls. If he calls on four potential clients, what is the probability that he makes exactly 3 sales? What is the probability that he makes exactly 4 sales?

Exercise 2

A special five football matches series will be played between UAE and KSA. The probability that UAE will win a match against KSA is 0.6.              

            (i). What is the probability that UAE will win at least 3 matches in the series?        

            (ii). What is the probability that UAE will lose all the matches of the series?          

            (iii). What is the probability that UAE will win at most 2 matches in the series?     

Exercise 2-34

Trowbridge Manufacturing produces cases for personal computers and other electronic equipment. The quality control inspector for this company believes that a particular process is out of control. Normally, only 5% of all cases are deemed defective due to   discolorations. If 6 such cases are sampled, what is the probability that there will be 0 defective cases if the process is operating correctly? What is the probability that there will be exactly 1 defective case?

Exercise 2-34

If 10% of all disk drives produced on an assembly line are defective, what is the probability that there will be exactly one defect in a random sample of 5 of these? What is the probability that there will be no defects in a random sample of 5?

Exercise 2-38

Steve Goodman, production foreman for the Florida Gold Fruit Company, estimates that the average sale of oranges is 4,700 and the standard deviation is 500 oranges. Sales follow a normal distribution.

(a)  What is the probability that sales will be greater than 5,500 oranges?

(b)  What is the probability that sales will be greater than 4,500 oranges?

(c)  What is the probability that sales will be less than 4,900 oranges?

(d) What is the probability that sales will be less than 4,300 oranges?

Exercise 2-41

The time to complete a construction project is normally distributed with a mean of 60 weeks and a standard deviation of 4 weeks.

(a)  What is the probability the project will be finished in 62 weeks or less?

(b) What is the probability the project will be finished in 66 weeks or less?

(c)  What is the probability the project will take longer than 65 weeks?

Exercise 2-42

A new integrated computer system is to be installed worldwide for a major corporation.  Bids on this project are being solicited, and the contract will be awarded to one of the bidders. As a part of the proposal for this project, bidders must specify how long the project will take. There will be a significant penalty for finishing late. One potential contractor determines that the average time to complete a project of this type is 40 weeks with a standard deviation of 5 weeks. The time required to complete this project is assumed to be normally distributed.

1. If the due date of this project is set at 40 weeks, what is the probability that the contractor will have to pay a penalty (i.e., the project will not be finished on schedule)?
2. If the due date of this project is set at 43 weeks what is the probability that the contractor will have to pay a penalty (i.e., the project will not be finished on schedule)?
3. If the bidder wishes to set the due date in the proposal so that there is only a 5% chance of being late (and consequently only a 5% chance of having to pay a penalty), what due date should be set?

Exercise 2-43

Patients arrive at the emergency room of Costa   Valley Hospital at an average of 5 per day. The demand for emergency room treatment at Costa Valley follows a Poisson distribution.

(a)  Using Appendix C, compute the probability of exactly 0, 1, 2, 3, 4, and 5 arrivals per day.

(b)  What is the sum of these probabilities, and why is the number less than 1?

Exercise 2-44

Using the data in Problem 2-43, determine the probability of more than 3 visits for emergency room service on any given day.

Blood type AB is found in only 3% of the population.† If 330 people are chosen at random, find the probability of the following. (Use the normal approximation. Round your answers to four decimal places.)

(a) 5 or more will have this blood type


(b) between 5 and 10 will have this blood type