Final Exam

FinalExam

Stacy Hatten

Started: December 7, 2011 5:51 PM

Questions: 60

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1. (Points: 1)

The Central Limit Theorem is important in statistics because _____.

1. for any size sample, it says the sampling distribution of the sample mean is

approximately normal

2. for any population, it says the sampling distribution of the sample mean is

approximately normal, regardless of the sample size

3. for a large n, it says the sampling distribution of the sample mean is approximately

normal, regardless of the population

4. for a large n, it says the population is approximately normal

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2. (Points: 1)

The registrar's office at State University would like to determine a 95% confidence interval for the mean commute time of its students. A member of the staff randomly chooses a parking lot and surveys the first 200 students who park in the chosen lot on a given day. The confidence interval is

1. not meaningful because the sampling distribution of the sample mean is not normal.

2. meaningful because the sample is representative of the population

3. not meaningful because of the lack of random sampling.

4. meaningful because the sample size exceeds 30 and the Central Limit Theorem ensures

normality of the sampling distribution of the sample mean.

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3. (Points: 1)

Page 1 of 26Assessment

12/7/2011https://vista.unm.edu/webct/urw/lc9522075409151.tp9522199562141/allViewAssessment....

A revenue department is under orders to reduce the time small business owners spend filling

out pension form ABC-5500. Previously the average time spent on the form was 5.2 hours. In order to test whether the time to fill out the form has been reduced, a sample of 65 small business owners who annually complete the form was randomly chosen, and their completion times

recorded. The mean completion time for ABC-5500 form was 4.8 hours with a standard deviation of 2.6 hours. In order to test that the time to complete the form has been reduced, state the appropriate null and alternative hypotheses.

1. H0: mu = 5.2 and Ha: mu not = 52

2. H0: mu > 52 and Ha: mu < 52

3. H0: mu = 52 and Ha: mu > 52

4. H0: mu >= 52 and Ha: mu < 52

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4. (Points: 1)

Given Ho: µ = 25, Ha :µ ≠ 25, and p = 0.033. Do you reject or fail to reject Ho at the .01

level of significance?

1. Reject H0

2. Fail to reject

3. Not sufficient information to decide

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5. (Points: 1)

A bottling company produces bottles that hold 8 ounces of liquid. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 36 bottles and finds the average amount of liquid held by the bottles

is 7.9155 ounces with a standard deviation of 0.30 ounce. Suppose the p-value of this test is 0.0455. State the proper conclusion.

1. At alpha - .05 reject the null hypothesis

2. At alpha = .025 reject the null hypothesis

3. At α = 0.085, fail to reject the null hypothesis.



4. At α = 0.035, accept the null hypothesis

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6. (Points: 1)

In a comprehensive road test on new car models, one variable measured is the time it takes the car to accelerate from 0 to 60 miles per hour. To model acceleration time, a regression

analysis is conducted on a random sample of 129 new cars.

TIME60 : y = Elapsed time (in seconds) from 0 mph to 60 mph

MAX x = Maximum speed attained (miles per hour)

The simple linear model E(y) = beta0 + beta1*x was fit to the data. Computer printouts for the analysis are given below:

NWEIGHTED LEAST SQUARES LINEAR REGRESSION OF TIME60

Predictor Variables Coefficient Std. Error t p-value

Constant 18.7171 .63708 29.38 .0000

MAX -.08365 .00491 -17.05 .0000

R-SQUARED = .6960; RESIDUAL MEAN SQ. (MSE) = 1.2869

ADJUSTED R-SQARED = .6937; STANDARD ERRO = 1.13444

Source df SS MS F p-val

Regression 1 374.285 374.285 290.83 .0000

Residual 127 163.443 1.28695

Total 123 537.728

CASES INCLUDED 129; MISSING CASES 0

Approximately what percentage of the sample variation in acceleration time can be explained by

the simple linear model?

1. 0%

2. -17%

3. 70%

4. 18.7%

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7. (Points: 1)



Parking at a university has become a problem. University administrators are interested in determining the average time it takes a student to find a parking spot. An administrator inconspicuously followed 160 students and recorded how long it took each of them to find a parking spot. Identify the population of interest to the university administration.

1. the 160 students about whom the data were collected

2. the entire set of faculty, staff, and students who park at the university

3. the students who park at the university between 9 and 10 AM on Wednesdays

4. the entire set of students who park at the university

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8. (Points: 1)

Suppose a large labor union wishes to estimate the mean number of hours per month a union member is absent from work. The union decides to sample 339 of its members at random and monitor the working time of each of them for 1 month. At the end of the month, the total number of hours absent from work is recorded for each employee. Which of the following should be used to estimate the parameter of interest for this problem?

1. A large sample confidence interval for mu

2. A small sample confidence interval for mu

3. A small sample confidence interval for p

4. A large sample confidence interval for p

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9. (Points: 1)

Explain what the phrase 95% confident means when we interpret a 95% confidence interval for µ.

1. The probability that the sample mean falls in the calculated interval is 0.95.

2. 95% of similarly constructed intervals would contain the value of the sampled mean.

3. 95% of the observations in the population fall within the bounds of the calculated

interval.



4. In repeated sampling, 95% of similarly constructed intervals contain the value of the

population mean.

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10. (Points: 1)

An insurance company sets up a statistical test with a null hypothesis that the average time for processing a claim is 3 days, and an alternative hypothesis that the average time for processing a claim is greater than 3 days. After completing the statistical test, it is concluded that the average time exceeds 3 days. However, it is eventually learned that the mean process time is really 3 days. What type of error occurred in the statistical test?

1. Type III error

2. Type II error

3. Type I error

4. No error occurred in the statistical sense.

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11. (Points: 1)

Solve the problem.

A state energy agency mailed questionnaires on energy conservation to 1,000 homeowners in

the state capital. Five hundred questionnaires were returned. Suppose an experiment consists of

randomly selecting one of the returned questionnaires. Consider the events:

A: {The home is constructed of brick} B: {The home is more than 30 years old}

In terms of A and B, describe a home that is constructed of brick and is less than or equal to 30 years old.

a. A B

b. A ∩ B

c. A ∩ Bc

d. (A ∩ B)c

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12. (Points: 1)

Solve the problem.

A company claims that 9 out of 10 doctors (i.e., 90%) recommend its brand of cough syrup to

their patients. To test this claim against the alternative that the actual proportion is less than

90%, a random sample of 100 doctors was chosen which resulted in 87 who indicate that they recommend this cough syrup. The test statistic in this problem is approximately:

a. -1.00

b. 1.00

c. -0.66

d. -0.50

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13. (Points: 1)

Solve the problem.

An industrial supplier has shipped a truckload of teflon lubricant cartridges to an aerospace

customer. The customer has been assured that the mean weight of these cartridges is in excess

of the 10 ounces printed on each cartridge. To check this claim, a sample of cartridges are randomly selected from the shipment and carefully weighed. Summary statistics for the sample

are: To determine whether the supplier's claim is true, consider the

test, H0: µ = 10 vs. where µ is the true mean weight of the cartridges. Find the

rejection region for the test using

a. t > 3.25, where t depends on 9 df

b. t > 2.821, where t depends on 9 df

c. z > 2.33

d. |z| > 2.58

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14. (Points: 1)

Solve the problem.

A lab orders a shipment of 100 frogs each week. Prices for the weekly shipments of frogs follow

the distribution below:



Suppose the mean cost of the frogs is $11.88 per week. Interpret this value.

a. The median cost for the distribution of frog costs is $11.88.

b. The average cost for all weekly frog purchases is $11.88.

c. Most of the weeks resulted in frog costs of $11.88.

d. The frog cost that occurs more often than any other is $11.88.

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15. (Points: 1)

Solve the problem.

Suppose a large labor union wishes to estimate the mean number of hours per month a union

member is absent from work. The union decides to sample 357 of its members at random and monitor the working time of each of them for 1 month. At the end of the month, the total

number of hours absent from work is recorded for each employee. Which of the following should be used to estimate the parameter of interest for this problem?

a. A large sample confidence interval for p.

b. A large sample confidence interval for µ.

c. A small sample confidence interval for p.

d. A small sample confidence interval for µ.

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16. (Points: 1)

Solve the problem.

A sports researcher is interested in determining if there is a relationship between the number of

home team and visiting team wins and different sports. A random sample of 526 games is

selected and the results are given below. Calculate the chi-square test statistic χ2 used to test

the claim that the number of home team and visiting team wins is independent of the sport. Use

α = 0.01.



a. 4.192

b. 2.919

c. 3.290

d. 5.391

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17. (Points: 1)

Solve the problem.

A cola manufacturer invited consumers to take a blind taste test. Consumers were asked to

decide which of two sodas they preferred. The manufacturer was also interested in what factors played a role in taste preferences. Below is a printout comparing the taste preferences of men

and women.

HYPOTHESIS: PROP. X = PROP. Y

SAMPLES SELECTED FROM soda(brand1,brand2)

males (sex=0, males) (NUMBER = 115)

females (sex=1, females) (NUMBER = 56)

X = males

Y = females

SAMPLE PROPORTION OF X = 0.422018

SAMPLE SIZE OF X = 109 SAMPLE PROPORTION OF Y = 0.25

SAMPLE SIZE OF Y = 52

PROPORTION X - PROPORTION Y = 0.172018

Z = 2.11825

Suppose the manufacturer wanted to test to determine if the males preferred its brand more

than the females. Using the test statistic given, compute the appropriate p-value for the test.

a. .0340

b. .0170

c. .4681

d. .2119

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18. (Points: 1)

Solve the problem.

How many tissues should a package of tissues contain? Researchers have determined that a

person uses an average of 50 tissues during a cold. Suppose a random sample of 10,000 people

yielded the following data on the number of tissues used during a cold: = 39, s = 15. Identify

the null and alternative hypothesis for a test to determine if the mean number of tissues used

during a cold is less than 50.

a. H0: µ = 50 vs. Ha: µ > 50

b. H0: µ > 50 vs. Ha: µ ≤ 50

c. H0: µ = 50 vs. Ha: µ < 50

d. H0: µ = 50 vs. Ha: µ ≠ 50

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19. (Points: 1)

Solve the problem.

Mamma Temte bakes six pies each day at a cost of $2 each. On 39% of the days she sells only

two pies. On 10% of the days, she sells 4 pies, and on the remaining 51% of the days, she sells all six pies. If Mama Temte sells her pies for $4 each, what is her expected profit for a day's

worth of pies? [Assume that any leftover pies are given away.]

a. $4.96

b. $16.96

c. -$7.76

d. -$8.00

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20. (Points: 1)

Solve the problem.

Consider the following set of salary data:



To determine if women have a higher mean salary than men, we would test:

a. H0: µ1 - µ2 = 0 vs. Ha: µ1 - µ2 = 0

b. H0: µ1 - µ2 = 0 vs. Ha: µ1 - µ2 < 0

c. H0: µ1 - µ2 = 0 vs. Ha: µ1 - µ2 > 0

d. H0: µ1 - µ2 = 0 vs. Ha: µ1 - µ2 ≠ 0

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21. (Points: 1)

Solve the problem.

A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a

mean of 470 seconds and a standard deviation of 60 seconds. The fitness association wants to

recognize the fastest 10% of the boys with certificates of recognition. What time would the boys need to beat in order to earn a certificate of recognition from the fitness association?

a. 393.2 seconds

b. 371.3 seconds

c. 546.8 seconds

d. 568.7 seconds

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22. (Points: 1)

Answer the question True or False.

The probability of success, p, in a binomial experiment is a parameter, while the mean and

standard deviation, µ and σ, are statistics.

a. True

b. False

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23. (Points: 1)



Solve the problem.

What is the probability associated with not making a Type II error?

a. (1 - β)

b. α

c. (1 - α)

d. β

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24. (Points: 1)

Solve the problem.

A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets, A, B, and C. Prices (in dollars) were recorded for a sample of 60

randomly selected grocery items at each of the three supermarkets. In order to reduce item-to-

item variation, the prices were recorded for each item on the same day at each supermarket.

Identify the treatments for this experiment.

a. the three supermarkets

b. the 60 grocery items

c. the day on which the data were collected

d. the 60 × 3 = 180 prices

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25. (Points: 1)


The sampling distribution for χ2 works well when expected counts are very small.



a. True

b. False

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26. (Points: 1)

Solve the problem.

An advertising firm conducts 11 different campaigns, each in 9 different cities, to promote a

certain product, and tracks the product sales attributable to each campaign in each city. Determine whether the experiment is observational or designed.

a. designed

b. observational

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27. (Points: 1)

Solve the problem.

An economy pack of highlighters contains 12 yellow, 6 blue, 4 green, and 3 orange highlighters.

An experiment consists of randomly selecting one of the highlighters and recording its color. Find the probability that a blue or yellow highlighter is selected given that a yellow highlighter is

selected.

a. 0

b. 1

c.

d.

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28. (Points: 1)

Solve the problem.

A teacher finds that final grades in the statistics department are distributed as: A, 25%; B,



25%; C, 40%; D, 5%; F, 5%. At the end of a randomly selected semester, the following grades

were recorded. Calculate the chi-square test statistic χ2 used to determine if the grade

distribution for the department is different than expected. Use α = 0.01.

a. 5.25

b. 3.41

c. 6.87

d. 4.82

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29. (Points: 1)

Solve the problem.

Consider the given discrete probability distribution. Find the probability that x exceeds 5.

a. 0.48

b. 0.52

c. 0.75

d. 0.27

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30. (Points: 1)

Solve the problem.

Find the following: P(F ≤ 2.71), for v1 = 5, v2 = 20

a. 0.975

b. 0.95



c. 0.05

d. 0.025

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31. (Points: 1)

Solve the problem.

Given H0: µ = 18, Ha: µ < 18, and p = 0.070. Do you reject or fail to reject H0 at the .05 level of

significance?

a. fail to reject H0

b. reject H0

c. not sufficient information to decide

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32. (Points: 1)

Solve the problem.

In a class of 40 students, 22 are women, 10 are earning an A, and 7 are women that are earning

an A. If a student is randomly selected from the class, find the probability that the student is a woman or earning an A.

a. .625

b. .8

c. .25

d. .975

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33. (Points: 1)

Solve the problem.

Data were collected from the sale of 25 properties by a local real estate agent. The following

printout concentrated on the land value variable from the sampled properties.

HYPOTHESIS: MEAN X = x



Find the p-value for testing whether the mean land value differs from $48,906.

a. p = 0.308142

b. p = 0.1918585

c. p = 0.0959288

d. p = 0.808142

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34. (Points: 1)

Solve the problem.

Given that the sum of squares for error (SSE) for an ANOVA F-test is 12,000 and there are 40

total experimental units with eight total treatments, find the mean square for error (MSE).

a. 300

b. 375

c. 400

d. 308

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35. (Points: 1)

Solve the problem.

A recent article in the paper claims that business ethics are at an all-time low. Reporting on a

recent sample, the paper claims that 33% of all employees believe their company president



possesses low ethical standards. Assume that responses were randomly and independently

collected. A president of a local company that employs 1,000 people does not believe the paper's claim applies to her company. If the claim is true, how many of her company's employees

believe that she possesses low ethical standards?

a. 330

b. 670

c. 967

d. 33

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36. (Points: 1)


The sample standard deviation of differences sd is equal to the difference of the sample standard

deviations

a. True

b. False

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37. (Points: 1)

Solve the problem.

If P(A B) = 1 and P(A ∩ B) = 0, then which statement is true?

a. A and B are supplementary events.

b. A and B are both empty events.

c. A and B are reciprocal events.

d. A and B are complementary events.

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38. (Points: 1)



Solve the problem.

Find a value of the standard normal random variable z, called z0, such that P(-z0 ≤ z ≤ z0) =

0.98.

a. 1.645

b. 1.96

c. 2.33

d. .99

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39. (Points: 1)

Solve the problem.

Use the appropriate table to find the following probability: P(χ2 > 16.75) for df = 5.

a. 0.005

b. 0.010

c. 0.995

d. 0.990

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40. (Points: 1)


When the sample size is small, confidence intervals for a population proportion are more reliable when the population proportion p is near 0 or 1.

a. True

b. False

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41. (Points: 1)



Solve the problem.

An insurance company sets up a statistical test with a null hypothesis that the average time for processing a claim is 4 days, and an alternative hypothesis that the average time for processing

a claim is greater than 4 days. After completing the statistical test, it is concluded that the

average time exceeds 4 days. However, it is eventually learned that the mean process time is really 4 days. What type of error occurred in the statistical test?

a. Type III error

b. No error occurred in the statistical sense.

c. Type I error

d. Type II error

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42. (Points: 1)

Solve the problem.

According to a recent study, 1 in every 6 women has been a victim of domestic abuse at some

point in her life. Suppose we have randomly and independently sampled twenty-five women and asked each whether she has been a victim of domestic abuse at some point in her life. Find the

probability that more than 22 of the women sampled have not been the victim of domestic

abuse.

a. 0.062896

b. 0.188687

c. 0.807120

d. 0.125791

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43. (Points: 1)

Solve the problem.

Which binomial probability is represented on the screen below?



a. The probability of 8 successes in 2 trials where the probability of success is .3.

b. The probability of 8 failures in 2 trials where the probability of failure is .3.

c. The probability of 2 successes in 8 trials where the probability of failure is .3.

d. The probability of 2 successes in 8 trials where the probability of success is .3.

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44. (Points: 1)

Solve the problem.

The number of cars running a red light in a day, at a given intersection, possesses a distribution with a mean of 2.2 cars and a standard deviation of 3. The number of cars running the red light

was observed on 100 randomly chosen days and the mean number of cars calculated. Describe

the sampling distribution of the sample mean.

a. approximately normal with mean = 2.2 and standard deviation = 3

b. shape unknown with mean = 2.2 and standard deviation = 0.3

c. approximately normal with mean = 2.2 and standard deviation = 0.3

d. shape unknown with mean = 2.2 and standard deviation = 3

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45. (Points: 1)

Solve the problem.

If a data set is normally distributed, what is the proportion of measurements you would expect

to fall within

a. 100%



b. 68%

c. 50%

d. 95%

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46. (Points: 1)

Solve the problem.

A random sample of 250 students at a university finds that these students take a mean of 15.7

credit hours per quarter with a standard deviation of 1.8 credit hours. Estimate the mean credit

hours taken by a student each quarter using a 98% confidence interval.

a. 15.7 ± .198

b. 15.7 ± .265

c. 15.7 ± .017

d. 15.7 ± .013

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47. (Points: 1)

Solve the problem.

Identify the rejection region that should be used to test against for

and

a. F > 6.76

b. F > 6.63

c. F > 3.69

d. F > 4.82

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48. (Points: 1)



Solve the problem.

Data was collected from CEOs of companies within both the low-tech industry and the consumer products industry. The following printout compares the mean return-to-pay ratios between CEOs

in the low-tech industry with CEOs in the consumer products industry.

HYPOTHESIS: MEAN X = MEAN Y

SAMPLES SELECTED FROM RETURN industry 1 (low tech) (NUMBER = 15)

industry 3 (consumer products) (NUMBER = 15) ___________________________________________________

X = industry1 Y = industry3

SAMPLE MEAN OF X = 157.286

SAMPLE VARIANCE OF X = 1563.45

SAMPLE SIZE OF X = 14 SAMPLE MEAN OF Y = 217.583

SAMPLE VARIANCE OF Y = 1601.54 SAMPLE SIZE OF Y = 12

MEAN X - MEAN Y = -60.2976 t = -4.23468

P-VALUE = 0.000290753

P-VALUE/2 = 0.000145377 SD. ERROR = 14.239

Using the printout, which of the following assumptions is not necessary for the test to be valid?

a. The population variances are equal.

b. The samples were randomly and independently selected.

c. Both populations have approximately normal distributions.

d. The population means are equal.

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49. (Points: 1)

Solve the problem.

Use the standard normal distribution to find P(-2.25 < z < 0).

a. .6831

b. .0122



c. .4878

d. .5122

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50. (Points: 1)

Solve the problem.

The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.54 ounces and a standard deviation of 0.36 ounce. Each can holds

a maximum of 12.90 ounces of soda. Every can that has more than 12.90 ounces of soda

poured into it causes a spill and the can must go through a special cleaning process before it can be sold. What is the probability that a randomly selected can will need to go through this

process?

a. .3413

b. .1587

c. .6587

d. .8413

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51. (Points: 1)

Solve the problem.

A random sample of n observations, selected from a normal population, is used to test the null

hypothesis H0: σ2 = 155. Specify the appropriate rejection region.

Ha: σ2 ≠ 155, n = 10, α = .05

a. χ2 < 3.32511 or χ

2 > 16.9190

b. χ2 < 2.70039 or χ

2 > 19.0228

c. χ2 < 3.24697 or χ

2 > 20.4831

d. 2.70039 < χ2 < 19.0228

Save Answer

52. (Points: 1)



Solve the problem.

Let t0 be a specific value of t. Find t0 such that the following statement is true:

P(t ≤ t0) = .01 where df = 20.

a. 2.539

b. -2.539

c. 2.528

d. -2.528

Save Answer

53. (Points: 1)

Solve the problem.

Which of the following statements is not a property of the normal curve?

a. symmetric about µ

b. P(µ - σ < x < µ + σ) ≈ .95

c. P(µ - 3σ < x < µ + 3σ) ≈ .997

d. mound-shaped (or bell shaped)

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54. (Points: 1)

Solve the problem.

A human gene carries a certain disease from a mother to her child with a probability rate of 0.47. That is, there is a 47% chance that the child becomes infected with the disease. Suppose a

female carrier of the gene has five children. Assume that the infections, or lack thereof, are independent of one another. Find the probability that all five of the children get the disease from

their mother.

a. 0.023

b. 0.042

c. 0.977



d. 0.037

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55. (Points: 1)


Sample statistics are random variables, because different samples can lead to different values of the sample statistics.

a. True

b. False

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56. (Points: 1)

Solve the problem.

A dice game involves rolling three dice and betting on one of the six numbers that are on the

dice. The game costs $9 to play, and you win if the number you bet appears on any of the dice.

The distribution for the outcomes of the game (including the profit) is shown below:

Find your expected profit from playing this game.

a. $9.19

b. -$1.23

c. $0.50

d. $4.93

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57. (Points: 1)


A rejection region is established in each tail of the sampling distribution for a two-tailed test.



a. True

b. False

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58. (Points: 1)


The mean of the standard normal distribution is 1 and the standard deviation is 0.

a. True

b. False

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59. (Points: 1)

Solve the problem.

A certain HMO is attempting to show the benefits of managed health care to an insurance

company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that primary specialty is an important factor in measuring the cost-effectiveness of

physicians. To investigate this, the HMO obtained independent random samples of 25 HMO physicians from each of four primary specialties-- General Practice (GP), Internal Medicine (IM),

Pediatrics (PED), and Family Physician (FP)-- and recorded the total per-member, per-month

charges for each. Identify the treatments for this group.

a. the HMO

b. the total per-member, per-month charges

c. the 100 physicians

d. the four specialty groups GP, IM, PED, and FP

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60. (Points: 1)

Solve the problem.

Which of the following represents the difference in two population proportions?



a.

b. p1 + p2

c. µ1 - µ2

d. p1 - p2

Save Answer

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