Questions
One generator is placed in standby redundancy to the main generator. The faliure rate of each...

One generator is placed in standby redundancy to the main generator. The faliure rate of each generator is estimated to be λ = 0.05/hr. Compute the reliability of the system for 10 hrs and its MTBF assuming that the sensing and switching device is 100% reliable. If the reliability of this device is only 80%, how are the results modified?

In: Math

PLEASE DO BY HAND AND NOT EXCEL 1.A car dealer believes that average daily sales for...

PLEASE DO BY HAND AND NOT EXCEL

1.A car dealer believes that average daily sales for four different dealerships in four separate states are equal. A random sample of days results in the following data on daily sales:

Ohio                New York       West Virginia              Pennsylvania

               3                          10                         3                                  20

               2                            0                         4                                  11

               6                            7                         5                                  8

               4                            8                                                             2

               4                            0                                                             14

               7

               2

Use ANOVA to test this claim at the 0.05 level.

In: Math

What does it mean to say that a particular result is statistically significant at the .05...

What does it mean to say that a particular result is statistically significant at the .05 level or at the .01 level? Is a result that is statistically significant at the .05 level automatically also significant at the .01 level? What about the reverse? Please explain your reasoning.

In: Math

1.   Do consumers spend more on a trip to Walmart or Target? Suppose researchers interested in...


1.   Do consumers spend more on a trip to Walmart or Target? Suppose researchers interested in this question collected a systematic sample from 85 Walmart customers and 80 Target customers by asking customers for their purchase amount as they left the stores. The data collected are summarized in the table below.
   
Walmart
Target
sample size
85
80
sample mean
$45
$53
sample std dev
$20
$18

a.   Check the conditions to create a confidence interval for the difference in spending at the two stores.
b.   Create a 95% confidence interval for the difference in spending at the two stores. (Note: We don’t have the full data, so you can use the formulas on page 342 or a program that doesn’t require it.)
c.   Interpret your confidence interval with a sentence.
d.   Your CI from part b does not contain zero. Does that mean the difference in spending at the two stores is statistically significant? Why or why not?

In: Math

We have:                     P(A) = 0.75                     P(

We have:

                    P(A) = 0.75

                    P(B|A) = 0.9

                    P(B|A′) = 0.8

                    P(C|A ∩ B) = 0.8

                    P(C|A ∩ B′) = 0.6

                    P(C|A′ ∩ B) = 0.7

                    P(C|A′ ∩ B′) = 0.3     

Compute:

              a) ?(?′| ?′)

              b) P (?′ ∪ ?′)

              c) ?(? ∩ ? ∩ ?)

              d) P(C)

              e) ?(? ∩ ? ∩ ?)’

              f) P(B)

              g) P(AUBUC)

In: Math

The life in hours of a thermocouple used in a furnace is known to be ap-...

The life in hours of a thermocouple used in a furnace is known to be ap-

proximately normally distributed, with standard deviation

σ

= 20 hours. A

random sample of 15 thermocouples resulted in he following data: 553, 552,

567, 579, 550, 541, 537, 553, 552, 546, 538, 553, 581, 539, 529.

Use the 5 steps in the testing procedure to solve following question:

a) Is there evidence to support the claim that mean life exceeds 540 hours?

Use a fixed-level test with

α

= 0

.

05.

b) What is the P-value for this test?

c) Construct a 95% one-sided lower CI on the mean life.

d) Use the CI found above to test the hypothesis.

e) What is the β-value for this test if the true mean life is 560 hours?

In: Math

PART 1. A study reports the following final notation: F (2, 12) = 5.00, p >...

PART 1.
A study reports the following final notation: F (2, 12) = 5.00, p > .05

a. How many samples were involved in this study?

b. How many total participants were involved in this study?

c. If MSwithin is 3, what is MSbetween?


PART 2.
Test the claim that the mean GPA for student athletes is higher than 3.1 at the .01 significance level.

Based on a sample of 50 people, the sample mean GPA was 3.15 with a standard deviation of 0.08

The test statistic is:  (to 3 decimals)

The p-value is:  (to 3 decimals)

Based on this we:

  • Fail to reject the null hypothesis
  • Reject the null hypothesis

In: Math

Total plasma volume is important in determining the required plasma component in blood replacement therapy for...

Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 40 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 7.80 ml/kg for the distribution of blood plasma.

(a)

Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.)

lower limitupper limitmargin of error

(b)

What conditions are necessary for your calculations? (Select all that apply.)

the distribution of weights is uniformσ is knownn is largethe distribution of weights is normalσ is unknown

(c)

Interpret your results in the context of this problem.

1% of the intervals created using this method will contain the true average blood plasma volume in male firefighters.The probability that this interval contains the true average blood plasma volume in male firefighters is 0.01.    The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99.99% of the intervals created using this method will contain the true average blood plasma volume in male firefighters.

(d)

Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.00 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)

male firefighters

In: Math

Steve is the director of operations for a diamond company. The company is considering whether to...

Steve is the director of operations for a diamond company. The company is considering whether to launch a new product​ line, which will require building a new facility. The research required to produce the new product has not been proven to work in a​ full-scale operation. If Steve decides to build the new facility and the process is​ successful, the company will earn a profit of 720,000. If the process is​ unsuccessful, his company will realize a loss of 900,000. Steve estimates that the probability of the​ full-scale process succeeding is 62%. Steve has the option of constructing a pilot plant for 59,000 to test the new process before deciding to build the​ full-scale facility. He estimates there is a 54% probability that the pilot plant will prove successful. If the pilot plant succeeds he thinks the chance of the full scale facility succeeding is 87%. if the pilot plant fails, he thinks the chance of the full scale facility succeeding is only 35%. Complete parts a, b, and c below.

A.) Construct a decision tree with all of the known information labeled

B.) Advise what to do ( should he build the pilot plant first?)

C.) what is the most they should pay to construct the pilot plant?

In: Math

A queuing system with a Poisson arrival rate and exponential service time has a single queue,...

A queuing system with a Poisson arrival rate and exponential service time has a single queue, two servers, an average arrival rate of 60 customers per hour, and an average service time of 1.5 minutes per customer.

The manager is thinking of implementing additional queues to avoid an overloaded system. What is the minimum number of additional queues required? Explain.

How many additional servers are required to ensure the utilization is less than or equal to 50%? Explain.

If the manager loses a server, what service time would be necessary to ensure that the queue length is not at risk of approaching infinity? Explain.

In: Math

In order to improve reliability: A. Repeat your measurements several times B. Take the average of...

In order to improve reliability:
A. Repeat your measurements several times
B. Take the average of several measurements
C. Use a better instrument
D. Both taking the average of several measurements and using a better instrument E. Both repeating your measurements several times and using a better instrument
12. The measured value considers:
A. True value
B. Bias
C. Random error
D. All of the choices are correct.
13. Measuring a healthy lifestyle. You want to measure the “healthiness” of college students’ lifestyles. Give an example of a clearly invalid way to measure healthiness. Then briefly describe a measurement process that you think is valid.
14. Rates versus counts. Thirty students in my Stat 1350 class last semester took Test 1 and 25 of them passed the test. Fifty-five students in my Stat 1350 WEB class last semester took Test 1 and 43 of them passed the test.
(a) More students in my WEB Stat 1350 class passed Test 1 than in my traditional Stat 1350 class. Why does this NOT show that my WEB students did better than my traditional students?
(b) What is the passing rate (percentage of students who passed) for each of my Stat 1350 classes?
WEB: __________________________________ Traditional: ______________________________
15. Obesity. An article in the June 30, 2010, Columbus Dispatch reported on the prevalence of obesity among adults in the 50 states. Based on information in the article, California has approximately 6.7 million obese adults, and Texas has approximately 5.2 million. On the other hand, Mississippi has a little over 730,000 obese adults. Do these numbers make a convincing case that California and Texas have a more substantial problem with obesity than Mississippi?

16. Measuring intelligence. “Intelligence” means something like “general problem-solving ability.” Explain why it is not valid to measure intelligence by a test that asks questions such as
Who wrote “The Star-Spangled Banner”? ______________________________________________________ Who won the last soccer World Cup? __________________________________________________________
17. Testing job applicants. The law requires that tests given to job applicants must be shown to be directly job related. The Department of Labor believes that an employment test called the General Aptitude Test Battery (GATB) is valid for a broad range of jobs. As in the case of the SAT, blacks and Hispanics get lower average scores on the GATB than do whites. Describe briefly what must be done to establish that the GATB has predictive validity as a measure of future performance on the job.
18. Validity, bias, reliability. This winter I went to a local pharmacy to have my blood pressure measured using a sophisticated electronic machine at the front of the store next to the checkout counter. Will the measurement of my blood pressure be biased? Reliable? Valid? Explain your answer.
19. More on bias and reliability. You cut 5 pieces of string having these lengths in inches: 2.9 9.5 5.7 4.2 7.6
A subject measures each length by eye. Make up a set of results from this activity that matches each of the descriptions below. For simplicity, assume that bias means the same fixed error every time rather than an “on the average” error in many measurements.
(a) The subject has a bias of 0.5 inch too long and is perfectly reliable. ___________ ___________ ___________ ___________ ___________
(b) The subject has no bias but is not perfectly reliable, so that the average difference in repeated measurements is 0.5 inch.
___________ ___________ ___________ ___________ ___________

(c) A subject measures the first length (true length = 2.9 inches) four times by eye. His measurements are 3.0 2.9 3.1 3.0
What are the four random errors for his measurements? ___________ ___________ ___________ ___________
20. The best earphones. You are writing an article for a consumer magazine based on a survey of the magazine’s readers that asked about satisfaction with mid-priced earphones for the iPod and iPhone. Of 1648 readers who reported owning the Apple in-ear headphone with remote and mic, 347 gave it an outstanding rating. Only 69 outstanding ratings were given by the 134 readers who owned Klipsch Image S4i earphones with microphone. Describe an appropriate variable, which can be computed from these counts, to measure high satisfaction with a make of earphone. Compute the values of this variable for the Apple and Klipsch earphones. Which brand has the better high-satisfaction rating?
21. Measuring pulse rate. You want to measure your resting pulse rate. You might count the number of beats in 5 seconds and multiply by 12 to get beats per minute. Why is this method less reliable than actually measuring the number of beats in a minute?
22. Measuring crime. Twice each year, the National Crime Victimization Survey asks a random sample of about 40,000 households whether they have been victims of crime and, if so, the details. In all, nearly 135,000 people answer these questions per year. If other people in a household are in the room while one person is answering questions, the measurement of, for example, rape and other sexual assaults could be seriously biased. Why? Would the presence of other people lead to over-reporting or underreporting of sexual assaults?

Lesson 3 – Making Sense of Numbers
23. A survey in a local newspaper stated that of the individuals who frequent bookstores, 14% were male and 28% were female. What is wrong with this picture?
A. Only 42% of the people were surveyed.
B. The percentages only add up to 42%. It should be 100%. C. There were twice as many females surveyed as males. D. 58% do not go to bookstores.
E. Nothing is wrong with this picture.
24. A newspaper reported "Approximately 17% of all crime takes place in the months of August and September." What is misleading about this statistic?
A. August and September are low points for crime statistically. B. It does not discuss the other months.
C. August and September make up 1/6 of the year which is 17%. D. None of the choices are correct.
25. Mark has two coupons—one for 10% off and one for $5 off. The store is allowing him to use both. He says to the cashier to apply the coupons in any order she wants because in the end it's the same amount off. Is he correct? (Hint: Try doing this for an item that is $100.)
A. Yes, it doesn't matter the way the coupons are applied.
B. No, you should apply the 10% off coupon first then apply the $5 off coupon. C. No, you should apply the $5 off coupon then apply the 10% off coupon.
D. You cannot determine from the information given.
26. When finding the percent change, your denominator should be:
A. Amount of change B. Starting value
C. The smaller value D. The larger value.
27. If an amount increases from 10 to 40 then the percent increase is:
A. 300% B. 400% C. 40% D. 10%
28. A newspaper reports "The percent decrease in the amount of wolves is 150%." What does this mean?
A. The amount of wolves has decreased in half.
B. There is 1/3 the amount of wolves that there has been previously. C. This is not possible. "Percent decrease" can't be more than 100%. D. None of the choices are correct.

29. What percentage of 30 is 40?
A. 133% B. 75% C. 13.3% D. 7.5%
30. The percent increase from 40 to 70 is:
A. 125% B. 75% C. 175% D. 25%
31. In determining if the numbers make sense you should:
A. Look at the context of the numbers and determine if there is missing information. B. Look for numbers that don't agree as they should.
C. Compare numbers and look for numbers that are surprisingly large or small.
D. All of the choices are correct.
E. None of the choices are correct.
32. Deer in the suburbs. Westchester County is a suburban area covering 433 square miles immediately north of New York City. A garden magazine claimed that the county is home to 800,000 deer. Do a calculation that shows this claim to be implausible.
33. Trash at sea? A report on the problem of vacation cruise ships polluting the sea by dumping garbage overboard said:
On a seven-day cruise, a medium-size ship (about 1,000 passengers and 1.000 crew members) might accumulate 222,000 coffee cups, 72,000 soda cans, 40,000 beer cans and bottles, and 11,000 wine bottles.
Are these numbers plausible? Do some arithmetic to back up your conclusion. Suppose, for example, that the crew is as large as the passenger list. How many cups of coffee must each person drink every day?

34. Airport delays. An article in a midwestern newspaper about flight delays at major airports said: According to a Gannett News Service study of U.S. airlines’ performance during the past five months,
Chicago’s O’Hare Field scheduled 114,370 flights. Nearly 10 percent, 1,136, were canceled.
Check the newspaper’s arithmetic. What percent of scheduled flights from O’Hare were actually canceled?
35. Battered women? A letter to the editor of the New York Times complained about a Times editorial that said “an American woman is beaten by her husband or boyfriend every 15 seconds.” The writer of the letter claimed that “at that rate, 21 million women would be beaten by their husbands or boyfriends every year. That is simply not the case.” He cited the National Crime Victimization Survey, which estimated 56,000 cases of violence against women by their husbands and 198,000 by boyfriends or former boyfriends. The survey showed 2.2 million assaults against women in all, most by strangers or someone the woman knew who was not her past or present husband or boyfriend.
(a) First do the arithmetic. Every 15 seconds is 4 per minute. At that rate, how many beatings would take place in an hour? In a day? In a year? Is the letter writer’s arithmetic correct?
(b) Is the letter writer correct to claim that the Times overstated the number of cases of domestic violence against women?
36. Stocks go down. On September 29, 2008, the Dow Jones Industrial Average dropped 778 points from its opening level of 11,143. This was the biggest one-day decline ever. By what percentage did the Dow drop that day? On October 28, 1929, the Dow Jones Industrial Average dropped 38 points from its opening level of 299. By what percentage did the Dow drop that day? This was the second-biggest one-day percentage drop ever.

37. Too good to be true? The late English psychologist Cyril Burt was known for his studies of the IQ scores of identical twins who were raised apart. The high correlation between the IQs of separated twins in Burt’s studies pointed to heredity as a major factor in IQ. (“Correlation” measures how closely two variables are connected. We will meet correlation in Chapter 14.) Burt wrote several accounts of his work, adding more pairs of twins over time. Here are his reported correlations as he published them:
What is suspicious here?

In: Math

PLEASE DO BY HAND AND NOT EXCEL Suppose we have the following data on variable X...

PLEASE DO BY HAND AND NOT EXCEL

  1. Suppose we have the following data on variable X (independent) and variable Y (dependent):

X         Y

2          70

0          70

4          130

a. Test to see whether X and Y are significantly related using a t-test on the slope of X. Test this at the 0.05 level.

b. Test to see whether X and Y are significantly related using an F-test on the slope of X. Test this at the 0.05 level.

In: Math

How well materials conduct heat matters when designing houses, for example. Conductivity is measured in terms...

How well materials conduct heat matters when designing houses, for example. Conductivity is measured in terms of watts of heat power transmitted per square meter of surface per degree Celsius of temperature difference on the two sides of the material. In these units, glass has conductivity about 1. The National Institution of Standards and Technology provides exact data on properties of materials. Here are 11 measurements of the heat conductivity of a particular type of glass.

1.11 1.05 1.12 1.07 1.13 1.07 1.08 1.15 1.17 1.18 1.13

(a) We can consider this an SRS of all specimens of glass of this type. Make a stemplot. (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.)

Stems Leaves

1.0 1.0 1.1 1.1

Is there any sign of major deviation from Normality?

The stemplot shows that the data are not skewed and have no outliers.

The stemplot shows that the data is skewed to the left with one outlier.

The stemplot shows that the data is skewed to the right with one outlier.

(b) Give a 80% confidence interval for the mean conductivity. (Use 3 decimal places.)

(__________ , __________)

In: Math

Conditional Probability Problem: An urn contains 5 red balls, 4 green balls, and 4 yellow balls...

Conditional Probability Problem: An urn contains 5 red balls, 4 green balls, and 4 yellow balls for a total of 13 balls. If 5 balls are randomly selected without replacement what is the probability of selecting at least two red balls given that at least one yellow ball is selected?

a) 0.59

b) 0.61

c) 0.63

d) 0.65

e) 0.67

In: Math

Share with your classmates the data visualisations you have created based on the sample data set,...

Share with your classmates the data visualisations you have created based on the sample data set, by posting screenshots of your charts and graphs on the class-wide forum. Reflect on how appropriate the different visualisations are for authentic representation of the data, and express which aspects of data visualisation play an important role in “telling the truth” about your data.

In: Math

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