*x*such that 6.3% of salmon flies live less than

_{0}*x*

_{0}days.

The lifetime of salmon flies is normally distributed with a mean of 60 days and a standard deviation of 20 days. Find the value *x*_{0} such that 6.3% of salmon flies live less than *x*_{0} days.

Tripp Cromer, President of Neverstop Travel claims that 40 percent of the company’s customers have taken at least one trip to Las Vegas. Tom Cruise, a veteran agent, suggests that Cromer’s claim is too low. The firm surveys 200 customers and finds that 84 have been to Vegas. Test the clai…

Week Four Homework Assignment – Forecasting

Ajax Manufacturing is an electronic test equipment manufacturing firm that markets a certain piece of specialty test equipment. Ajax has several competitors who currently market similar pieces of equipment.

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Week Four Homework Assignment – Forecasting

Ajax Manufacturing is an electronic test equipment manufacturing firm that markets a certain piece of specialty test equipment. Ajax has several competitors who currently market similar pieces of equipment. While customers have repeatedly indicated they prefer Ajax’s test equipment, they have historically proven to be unwilling to wait for Ajax to manufacture this certain piece of equipment on demand and will purchase their test equipment from Ajax’s competitors in the event Ajax does not have the equipment available in inventory for immediate delivery. Thus, the key to Ajax successfully maintaining market share for this particular piece of equipment has been to have it available in stock for immediate delivery. Unfortunately, it is a rather expensive piece of equipment to maintain in inventory. Thus, the president of Ajax Manufacturing is very interested in accurately forecasting market demand in order to ensure he has adequate inventory available to meet customer demand without incurring undue inventory costs. His sales department has provided the following historical data regarding market demand for this certain piece of specialty electronics test equipment for the past 24 months.

Time Period

Actual Number of Units Sold

1

33

2

36

3

32

4

35

5

33

6

36

7

34

8

38

9

37

10

36

11

38

12

38

13

37

14

39

15

35

16

38

17

37

18

39

19

37

20

35

21

37

22

34

23

35

24

36

Hint: For questions 23 through 25, you need to keep in mind that the projected demand for the test equipment for time period 25 derived by the forecasting model is only a point estimate (this concept was discussed in week one relative to the mean). While a point estimate is a precise value, it is not necessarily an accurate value since the various measures of forecasting accuracy (i.e., MAD, MSE and MAPE) tell us there is some potential degree of error…

to

remain in the presidental pool timmy must be placed in the middle 50%

on a regional pool. if the mean for the pool is 100 and the SD is 15,

find the two limits (upper and lower) or the scores that would enable

timmy to remain in the race. Assume the distribution is normal

remain in the presidental pool timmy must be placed in the middle 50%

on a regional pool. if the mean for the pool is 100 and the SD is 15,

find the two limits (upper and lower) or the scores that would enable

timmy to remain in the race. Assume the distribution is normal

Suppose we are interested in

the condition of a machine that produces a particular item. Let *A*designate the event “the machine

is in good operating condition”; then represents “the machine is not in good operating

condition.” We might know from experience that the machine is in good

condition 90% of the time.

Given the machine’s

condition, we might also know the probability that a defective item will be

produced (event B*).*Suppose that,

when the machine is in good condition, only 1% of the items produced are

defective, while 10% are defective when the machine is in poor condition.

1.What is the probability of selecting a defective item?

**Make sure to show your work**.

**(.90)(.01)+ (.10)(.10) = 1.9%**

2.What is the probability of selecting a defective item

from the machine in good condition? **Make
sure to show your work**.

3.Suppose that, without knowing the condition of the

machine, we select an item from the current production run and observe that it

is defective. What is the probability that it came from the machine that is in

good condition? Comment on how the prior probability was revised in the light

of the new information. **Make sure to
show your work**.

4.If we select an item from the current production run

and observe that it is defective, what is the probability that it came from the

machine that is in poor condition? Comment on how the prior probability was

revised in the light of the new information. **Make sure to show your work**.

5.What is the probability of selecting a non-defective

item? **Make sure to show your work**.

6.What is the probability of selecting a non-defective

item from the machine in good condition? **Make
sure to show your work**.

7.Suppose that, without knowing the condition of the

machine, we select an item from the current production run and observe that it

is not defective. What is the probability that it came from the machine that is

in good condition? Comment on how the prior probability was revised in the

light of the new information. **Make sure
to show your work**.

8.If we select an item from the current production run

and observe that it is not defective, what is the probability that it came from

the machine that is in poor condition? Comment on how the prior probability was

revised in the light of the new information. **Make sure to show your work**.

2. The following table represents the U.S. sources of electrical energy:Source Number of plantCoal50Hydropower7Natural Gas18Nuclear20Oil3Renewables2a. Represent the table in a bar chart using frequencies.b. Construct a pie chart using percentages.c. Construct a Pareto chart also showing the cumulative percentage.3. The following data represents the number of days between the receipt of the complaint and the resolution of the complaint:54 4 35 137 31 27 152 2 123 81 74 27 11 19 126 110 110 29 61 35 94 31 26 5 12 4 16532 29 28 29 26 25 1 14 13 13 10 5 27 4 52 30 22 36 26 20 23 33 68a.

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2. The following table represents the U.S. sources of electrical energy:Source Number of plantCoal50Hydropower7Natural Gas18Nuclear20Oil3Renewables2a. Represent the table in a bar chart using frequencies.b. Construct a pie chart using percentages.c. Construct a Pareto chart also showing the cumulative percentage.3. The following data represents the number of days between the receipt of the complaint and the resolution of the complaint:54 4 35 137 31 27 152 2 123 81 74 27 11 19 126 110 110 29 61 35 94 31 26 5 12 4 16532 29 28 29 26 25 1 14 13 13 10 5 27 4 52 30 22 36 26 20 23 33 68a. Construct a frequency distribution and a percentage distribution.b. Construct a histogram and a percentage polygon.c. Form a cumulative percentage distribution and plot a cumulative percentage polygon.d. What would you tell the president of company about how long a costumer should expect to wait for the complaint to be resolved?4. The following data was collected on the weight of hammers:234 245 312 457 590 345 820 622 710 189 299 500 478 1000 430 836 439 444a. Compute the mean, median, and mode.b. Compute the range, variance, standard deviation, and coefficient of variation.c. Compute Z-scores. Are there any outliers?d. Describe the shape of the data set.5. Given the following data: 58 63 41 42 29 50 62 43 40 34 70 63 55a. Compute the first quartile, the third quartile, and the interquartile range.b. List the five-number summary.c. Construct a boxplot and describe the shape.6.below is data from a drug cocktail showing the dependence of viscosity on protein concentration.protein concentration(mg/ml)viscosity(cps)251.2507.47512.110020.0a.compute the covariance between protein concentration and viscosity?b.compute the coefficient of correlation between protein concentration and viscosity?7.A survey found that in a sample of 189 large companies,40 offered stock options to their board members as part of their non-cash compensation packages.For small-to-midsized companies,43 of 180 surveyed…

State the null and alternative hypotheses.

Is there a linear relationship between annual per capita sugar consumption (in kilograms) and the average number of cavities of 11- and 12-year-old children in seven countries? The data is listed below.

Sugar Consumption, x

2.1

5.0

6.3

6.5

7.7

8.7

11.6

Is there a linear relationship between annual per capita sugar consumption (in kilograms) and the average number of cavities of 11- and 12-year-old children in seven countries? The data is listed below.

Sugar Consumption, x

2.1

5.0

6.3

6.5

7.7

8.7

11.6

Cavities, y

0.5…

The U.S. Department of Education reported that for the past seven years 4,033, 5,652, 6,407, 7,201, 8,719, 11,154, and 15,121 people received bachelor’s degrees in computer and information sciences. What is the arithmetic mean annual number receiving this degree?

Answer

About 12,240

About 8,327

About 6,…

Answer

About 12,240

About 8,327

About 6,…

For each of the situations in parts below, each random variable follows a binomial distribution. Give the parameters for each situation.

(c) Under the set-up of part (b), define the random variable Y to be the number of experiments that do not succeed.

((b) A scientist attempts to perform a difficult …

A scientist attempts to perform a difficult experiment. She is successful in about 80% of her attempts. She attempts the experiment 6 times.

What is the probability that at least one of the attempts will be a success?

A town has two community swimming pools. A random sample of season-pass holders from each pool found that 16 of 42 swimmers from the North Pool and 21 of 36 swimmers from the South Pool suffered an ear infection in the last year. At the ? = 0.05 level of significance, is there sufficient evidence to…

Approx. 40% of the Wisconsin population have type O blood. If 4 persons are selected at random to be donors, find P(at least one type O). PLEASE SHOW WORK!

A study determines that there is a strong positive correlation in the U. S. between teachers’ salaries and annual consumption of liquor. Which of the following statements is the most valid conclusion?

What is the 25th percentile of a X2 distribution with 20 degrees of freedom? What symbol is used to denote this value?

Assignment #2: Inference Using t for Inference

Name_____________________________ Due: Jan 18, 2012

1. The volume of Google stock is the number of shares traded on a given day. The following data is in millions of shares which mean that 4.6 represents 4,600,000 stocks traded. The following data is generated from a random sample of trading days in 2004.

4.64

7.57

7.49

5.54

21.16

13.36

3.11

3.55

15.27

2.60

22.31

11.19

11.90

4.57

19.83

13.89

6.60

14.85

2.03

2.50

3.91

10.64

6.26

7.57

3.93

9.14

8.77

5.52

7.03

14.41

16.75

8.47

5.

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Assignment #2: Inference Using t for Inference

Name_____________________________ Due: Jan 18, 2012

1. The volume of Google stock is the number of shares traded on a given day. The following data is in millions of shares which mean that 4.6 represents 4,600,000 stocks traded. The following data is generated from a random sample of trading days in 2004.

4.64

7.57

7.49

5.54

21.16

13.36

3.11

3.55

15.27

2.60

22.31

11.19

11.90

4.57

19.83

13.89

6.60

14.85

2.03

2.50

3.91

10.64

6.26

7.57

3.93

9.14

8.77

5.52

7.03

14.41

16.75

8.47

5.84

a) Use a normal probability plot to determine if the data is sampled from a normally distributed population.

b) Use a box plot to determine if there are any outliers.

c) Use the data to construct a 90% confidence interval estimate for the population mean of the number of shares traded per day in 2004.

b) Use the confidence interval to test the hypothesis if the population mean is 11.1 million shares.

2. The online article âThe USA Junior Chess Olympics Research: Developing Memory and Verbal Reasoningâ (New Horizons for Learning, April 2001: available at www.newhorizons.org) describes a study in which sixth graders who had not previously played chess participated in a program where they took chess lessons and played chess daily for 9 months. Each student took a memory test (the Test of Cognitive Skills) before starting the chess program and again at the end of the 9-months. Data is below. The author of the article proposed using these data to test the theory that students who participate in a chess program tend to achieve higher memory scores after completing the program.

Student # Pretest score Post test score

1 510 850

2 610 790

3 640 850

4 675 775

5 600 700

6 550 775

7 610 700

8 625 850

9 450 690

10 720 775

11 575 540

12 675 680

Conduct a test using the appropriate formula…

a young adult was chosen at random. the probability is .12 that the person chosen did not complete high school, .31 that he has a HS diploma but no further education. and .29 he has at least a BA. (a) what must the probability be that he has an education beyond HS but not a BA degree? (b) what is the probability that he has at least a HS education?

1. Following table shows unit profit matrix of transportation:-

To ai

(Units)

W1 W2 W3 W4 W5

From F1 105 120 140 170 65 600

F2 69 109 125 137 142 250

F3 149 165 170 92 87 150

bj (Units) 100 50 500 75 275 1000

To ai

(Units)

W1 W2 W3 W4 W5

From F1 105 120 140 170 65 600

F2 69 109 125 137 142 250

F3 149 165 170 92 87 150

bj (Units) 100 50 500 75 275 1000

Determine total profit by a. NWCR b. VAM

True/False questions

True/False

Chapter 7

1. A sample size of 1000 is large enough to use normal approximation for the distribution of p, when the estimate of the population proportion is .990.

2. For any sampled population, the population of all sample means is not always normally distributed.

3. The mean of the sampling distribution of is always not always equal to the mean of the sampled population.

4. The standard deviation of all possible sample proportions decreases as the sample size increases.

Chapter 8

5. Assuming the same significance level?, as the sample size increases, the value of t?/2 becomes smaller and smaller and approaches the corresponding value of z?/2.

6. First a confidence interval is constructed without using the finite population correction factor. Then, for the same identical data, a confidence interval is constructed using the finite population correction factor. The width of the interval without the finite population correction factor is narrower than the confidence interval with the finite population correction factor.

7. When the level of confidence and sample standard deviation remain the same, a confidence interval for a population mean based on a sample of n=100 will be wider than a confidence interval for a population mean based on a sample of n = 150.

8. When the level of confidence and the sample size remain the same, a confidence interval for a population mean Âľ will be narrower, when the sample standard deviation s is larger than when s is small.

True/False

Chapter 7

1. A sample size of 1000 is large enough to use normal approximation for the distribution of p, when the estimate of the population proportion is .990.

2. For any sampled population, the population of all sample means is not always normally distributed.

3. The mean of the sampling distribution of is always not always equal to the mean of the sampled population.

4. The standard deviation of all possible sample proportions decreases as the sample size increases.

Chapter 8

5. Assuming the same significance level?, as the sample size increases, the value of t?/2 becomes smaller and smaller and approaches the corresponding value of z?/2.

6. First a confidence interval is constructed without using the finite population correction factor. Then, for the same identical data, a confidence interval is constructed using the finite population correction factor. The width of the interval without the finite population correction factor is narrower than the confidence interval with the finite population correction factor.

7. When the level of confidence and sample standard deviation remain the same, a confidence interval for a population mean based on a sample of n=100 will be wider than a confidence interval for a population mean based on a sample of n = 150.

8. When the level of confidence and the sample size remain the same, a confidence interval for a population mean Âľ will be narrower, when the sample standard deviation s is larger than when s is small.

Multiple choices

Chapter 7

1. According to a hospital administrator, historical records over the past 10 years have shown that 20% of the major surgery patients are dissatisfied with after-surgery care in the hospital. A scientific poll based on 100 hospital patients has just been conducted.

Sixty-four (64) patients indicated that they were dissatisfied with the after surgery care. What are the mean and the standard deviation of the sampling distribution of p ?

A. 16% and .034%

B. 20% and .10%

C. 20% and 2%

D. 20% and .034%

E. 20% and 4%

2. If the sampled population has a mean 48 and standard deviation 4, then the Mean and the Variance for the sampling distribution of for n=25 are:

A. 3 and 4

B. 12 and 4

C. 48 and .64

D. 48 and 3.2

E. 48 and 16

3. If a population distribution is known to be normal, then it follows that:

A. The sample mean must equal the population mean

B. The sample mean must equal the population mean for large samples

C. The sample proportion must equal the population proportion

D. All of the above

E. None of the above

4. A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population mean and standard deviation of 90 lbs. and 24 lbs. respectively, then based on a sample size of 36 boxes, the probability that the average weight of the boxes will be less than 94 lbs. is:

A. 34.13%

B. 84.13%

C. 15.87%

D. 56.36%

E. 16.87%

5. The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent more than 90 days overdue. The historical records of the company show that over the past 8 years 13 percent of the accounts are delinquent. For this quarter, the auditing staff randomly selected 250 customer accounts. What is the probability that more than 40 accounts will be classified as delinquent?

A. 42.07%

B. 92.07%

C. 7.93%

D. 40.15%

E. 90.15%

Chapter 8

6. The width of a confidence interval will be:

A. Narrower for 99% confidence than 95% confidence

B. Narrower for a sample size of 100 than for a sample size of 50

C. Wider for 90% confidence than 95% confidence

D. Wider when the sample standard deviation (s) is large than when s is small

7. As standard deviation decreases, samples size _____________ to achieve a specified level of confidence.

A. Increases

B. Decreases

C. Remains the same

8. In a manufacturing process a random sample of 9 bolts manufactured has a mean length of 3 inches with a standard deviation of .3 inches. What is the 90% confidence interval for the true mean length of the bolt?

A. 2.804 to 3.196

B. 2.308 to 3.692

C. 2.769 to 3.231

D. 2.412 to 3.588

E. 2.814 to 3.186

9. The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are current (between 0 and 60 days after billing). The historical records show that over the past 8 years 60 percent of the accounts have been current. Determine the sample size needed in order to be 95% confident that the sample proportion of the current customer accounts is within .02 of the true proportion of all current accounts for this company.

A. 2305

B. 1549

C. 2800

D. 3981

E. 1624

Essay type

Chapter 7

1. In the upcoming governor’s election, the most recent poll based on 900 respondents to predict whether the incumbent will be reelected. For the sake of argument, assume that 55% of the actual voters in the state support the incumbent governor (p=0.55). Calculate the probability of observing a sample proportion of voters 0.50 or higher supporting the incumbent governor.

2. The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.3 inches. A sample of 9 metal sheets is randomly selected from a batch. What is the probability that the average length of a sheet is between 30.25 and 30.35 inches long?

Chapter 8

3. Recently, a case of food poisoning was traced to a particular restaurant chain. The source was identified and corrective actions were taken to make sure that the food poisoning would not reoccur. Despite the response from the restaurant chain, many consumers refused to visit the restaurant for some time after the event. A survey was conducted three months after the food poisoning occurred with a sample of 319 patrons contacted. Of the 319 contacted, 29 indicated that they would not go back to the restaurant because of the potential for food poisoning. What sample size would be needed in order to be 99% confident that the sample proportion is within .03 of p, the true proportion of customers who refuse to go back to the restaurant?

4. In a poll of 1,004 adults, 93% indicated that restaurants and bars should refuse service to patrons who have had too much to drink. Construct the 95% confidence interval for the proportion of all adults who feel the same way.

True/False questions True/False Chapter 7 1. A sample size of 1000 is large enough to use normal approximation for the distribution of p, when the estimate of the population proportion is .990. 2. For any sampled population, the population of all sample means is not always normally distributed.

3. The mean of the sampling distribution of is always not always equal to the mean of the sampled population. 4. The standard deviation of all possible sample proportions decreases as the sample size increases. Chapter 8

5.

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True/False questions True/False Chapter 7 1. A sample size of 1000 is large enough to use normal approximation for the distribution of p, when the estimate of the population proportion is .990. 2. For any sampled population, the population of all sample means is not always normally distributed.

3. The mean of the sampling distribution of is always not always equal to the mean of the sampled population. 4. The standard deviation of all possible sample proportions decreases as the sample size increases. Chapter 8

5. Assuming the same significance level, as the sample size increases, the value of t/2 becomes smaller and smaller and approaches the corresponding value of z/2. 6. First a confidence interval is constructed without using the finite population correction factor. Then, for the same identical data, a confidence interval is constructed using the finite population correction factor. The width of the interval without the finite population correction factor is narrower than the confidence interval with the finite population correction factor. 7. When the level of confidence and sample standard deviation remain the same, a confidence interval for a population mean based on a sample of n=100 will be wider than a confidence interval for a population mean based on a sample of n = 150. 8. When the level of confidence and the sample size remain the same, a confidence interval for a population mean µ will be narrower, when the sample standard deviation s is larger than when s is small.

Multiple choices

Chapter 7 1. According to a hospital administrator, historical records over the past 10 years have shown that 20% of the major surgery patients are dissatisfied with after-surgery care in the hospital. A scientific poll based on 100 hospital patients has just been conducted. Sixty-four (64) patients indicated that they were dissatisfied with the after surgery care. What are the mean and the standard deviation of the sampling distribution of p ? A. 16%…

The College Boards are administered each year to thousands of high school seniors, and these

scores are approximately normally distributed with a mean of 500, and a standard deviation of 100.

Suppose a random sample of 100 students was drawn and the mean exam score was 545 with standard

deviation of 49. Is the 45 point difference between the sample and the population merely due to

chance? Use the appropriate two-tailed test with an a = 0.05.

scores are approximately normally distributed with a mean of 500, and a standard deviation of 100.

Suppose a random sample of 100 students was drawn and the mean exam score was 545 with standard

deviation of 49. Is the 45 point difference between the sample and the population merely due to

chance? Use the appropriate two-tailed test with an a = 0.05.