1. Suppose a random sample of 36 items is selected from a population. The population

standard deviation is known to be 10. The standard error ofthe mean would be:

(a) 1.333

(b) 1.667

(c) 3.667

(d) 2.333

(e) 1.875

2. From 100 homes of similar sizes, a sample of 25 homes is selected to study the average

home heating cost during the winter months. Suppose the heating cost is known to be

normally distributed with mean of $220 per month for the four months of winter and

standard deviation of $45. Ifthe 100 homes represent the population size, the standard

error of the heating cost would be:

(a) 9.00

(b) 8.75

(c) 3.66

(d) 7.83

(e) 1.87

3. Suppose n=64 measurements is selected from a population with mean #220 and

standard deviation 0′ =16 . The Z-score corresponding to a value of x = 24 would be:

(a) 2.0

(b) 3.0

(c) -2.5

(d) -2.0

(e) 1.5

l. A random sample of n=100 observations is selected from a population with y = 30 and

standard deviation 0′ =16 . The probability that p()-c 2 28) is

(a) 0.8236

(b) 0.8936

(c) 0.9036

(d) 0.9983

(e) 0.8944

i. A random sample of n=100 observations is selected from a population with y = 30 and

standard deviation 0′ =16 . The probability that p(22.1< ; < 26.8) is

(a) 0.0434

(b) 0.0228

(c) 0.0036

(d) 0.0983

(e) 0.0944

3. A random sample of size 36 is drawn from a population with meany = 278. If 86% of

the time the sample mean is less than 281, then the population standard deviation

would be:

(a) 16.67

(b) 12.67

(c) 11.12

(d) 13.33

(e) 19.67

A random sample of size n=81 is drawn from population with mean equal to 50 and

standard deviation 25. The expected value ofthe mean E(xi) [or, y;] and the standard

errora;

(a) 50 and 2.95

(b) 50 and 2.78

(c) 28 and 1.72

(d) 50 and 15.00

(e) 80 and 12.0

According to a recent news report, the average price of gasoline is $3.80 per gallon

(March 2011). This price can be considered as the nationwide population mean price

per gallon. Suppose that the standard deviation of the gasoline price per gallon is

$0.50. A sample of 49 gas stations in Salt Lake City is taken. The probability that the

sample mean price is within $0.10 of the population mean is

(a) 0.9236

(b) 0.8384

(c) 0.9544

(d) 0.9983

(e) 0.8764

9. A finite population is normally distributed with mean #250 and standard deviation

0′ =15. Suppose a sample of size 49 is taken so that the sample mean )-c can be used to

estimate the population mean y. The probability that the sample mean is less than or

equal to 48 or, p(; S 48) ifthe size ofthe finite population is N=150

(a) 0.1236

(b) 0.2420

(c) 0.1544

(d) 0.1983

(e) 0.1292

10. The average life of a battery used in newly designed electric cars is 150 hours with a

standard deviation of 20 hours. Suppose these values are true for all batteries of this

type so that these values can be considered true for the population with u = 150 and o

20. If a sample of size 50 is selected, the probability that the sample mean life is

within i 5 of the population mean (between 145 and 155 hours) is

(a) 0.8236

(b) 0.9420

(c) 0.9544

(d) 0.9232

(e) 0.1292

11. The production manager of a bottling plant has acquired new machines to fill beverage

cans. These machines are used to fill 16 ounce cans in one of their production lines. If

the filling machine is working properly, the mean fill volume should be 16.0 ounces

with a standard deviation of 0.30 ounces. If mean fill volume in the cans is over 16.2

ounces or below 15.8 ounces, then an over filling or under filling occurs. To avoid over

or under filling the production manager randomly selects a sample of 9 cans

periodically and checks the volume. If the average content is less than 15.8 ounces or

more than 16.2 ounces, the production manager must stop the line to make

adjustments. The probability of stopping the line based on the information above is:

(a) 0.0236

(b) 0.0376

(c) 0.0400

(d) 0.0456

(e) None ofthe above

12. A new Rasmussen Report national telephone survey finds that just 32% of American

Adults favor “sin taxes” on soda and junk foods. The survey was based on a sample of

1,000 American Adults. Based on this survey data, the standard deviation of For the

standard error of sample proportion would be (considering p = 0.32)

(a) 0.0176

(b) 0.0200

(c) 0.0196

(d) 0.0148

(e) 0.0138

13. Based on a report, 55% of the voters believe that the nation’s current economic

problems are the result of recession that started during the Bush administration. A

new Rasmussen Reports national telephone survey finds that 51% of likely voters say

the nation’s current economic problems are due to the recession which began under

the administration of George Bush. This survey was based on 1,000 likely voters and

was conducted on March 18-19, 2011 by Rasmussen Reports. Based on this survey

report, the probability that the sample proportion is lower than 51% is approximately

(a) 0.0076

(b) 0.0200

(c) 0.0055

(d) 0.0098

(e) 0.0128

14. According to a newly published report approximately 43% of adults say filing their

tax paperwork is worse than a trip to the dentist. If a random sample of 200 is

chosen, the probability that at least 90 of them share this opinion is

(a) 0.2076

(b) 0.3200

(c) 0.0155

(d) 0.2843

(e) 0.3128

15.A study about the students graduating within 4 years of their entrance to the

universities indicated that 62% of the students do not graduate within 4 years.

Suppose a random sample of 500 students was taken. The sample considered the

students after 4 years of their college entrance. The probability that fewer than 285

graduated within 4 years is

(a) 0.4893

(b) 0.9893

(c) 0.0107

(d) 0.0584

(e) 0.0628

16. Historically, a production line produces 6% defective items. The production

supervisor takes a sample of 100 items frequently and if he finds 8 or more defective

products, he stops the line to make adjustments. The probability that a random

sample of 100 would lead to the stoppage ofthe production line is:

(a) 0.2995

(b) 0.3893

(c) 0.2005

(d) 0.4584

(e) 0.7995

17. In simple random sampling

(a) Every sample has equal probability being selected

(b) Every sample is drawn at a pre-specified time

(c) Every item in the sample has equal probability

(d) None ofthe above is correct

(e) Only (a) and (c) are correct

18. From a population of size 8 (N=8), all possible samples of size 3 (n=3) that can be drawn

are:

(a) 24

(b) 15

(c) 10

(d) 56

(e) 86

19. A confidence interval for the mean is determined using the following formula

Ei1.28[ij

J;

The confidence level being used in the above interval is

(a) 95%

(b) 98%

(c) 99%

(d) 67%

(e) 80%

20. A confidence interval for the mean is determined using the following formula

xio.99[£]

J2

The confidence level being used in the above interval is

(a) 95.52%

(b) 98.32%

(c) 33.89%

(d) 67.78%

(e) 80.56%

21. In a confidence interval, increasing the confidence level while keeping the sample size

fixed

(a) increases the width of the confidence interval.

(b) leaves the confidence interval unchanged.

(c) makes the confidence interval estimate more precise.

(d) makes the confidence interval estimate more reliable.

(e) decreases the width of the confidence interval.

22. The general form of a confidence interval is

(a) Point estimate i standard error.

(b) Mean i standard error ofthe mean.

(c) Mean i the margin of error.

(d) Point estimate i the margin of error.

(e) Estimate i the margin of error.

23.A random sample of n measurements is selected from a population with unknown

mean y and known standard deviation 0′. A 95% confidence interval for y when

n = 200,} 2102,0′ = 4.69 would be

(a) 104.35 and 15.65.

(b) 103.76 and 134.24

(c) 101.35 and 102.65

(d) 108.56 and 120.44

(e) 118.25 and 123.75

24. A random sample of size 20 produced a sample mean $232.8 and a standard

deviation 5 = 3.6. A 80% confidence interval using a t-distribution is to be constructed.

The t- value for the interval would be

(a) 1.711

(b) 2.064

(c) 2.038

(d) 1.328

(e) 2.485

25. In constructing a confidence interval with known population standard deviation 0 the

sample size is increased from n=36 to n=144 while the confidence level is held fixed at

95%. This will

(a) increase the width of the confidence interval making the estimate less precise.

(b) decrease the width ofthe confidence interval making the estimate less precise.

(c) leave the width ofthe confidence interval unchanged.

(d) double the width of the confidence interval.

(e) decrease the width of the confidence interval making the estimate more precise.

26. In constructing a confidence interval with known population standard deviation

(0′ = 8), the sample size is increased from n=64 to n=256 while the confidence level is

held fixed at 95%. This will

(a) decrease the width of the confidence interval by 75%.

(b) leave the width of the confidence interval unchanged.

(c) double the width of the confidence interval.

(d) reduce the width of the interval to one-half.

(e) Increase the width ofthe interval by 100%.

27. The length of time that a space rocket component functions is approximately normally

distributed. A sample of 20 of these components showed a mean of $2900 hours

with a standard deviation 5 = 87 hours. A 95% confidence interval for the mean time

that the component will function is to be constructed. The margin of error would be

(a) 42.9

(b) 40.7

(c) 81.4

(d) 34.2

(e) Can’t be determined

28. The length of time that a space rocket component functions is approximately normally

distributed. A sample of 20 of these components showed a mean of $2900 hours

with a standard deviation 5 = 87 hours. A 95% confidence interval for the mean time

that the component will function

(a) 824.94 to 927.06

(b) 724.94 to 927.46

(c) 823.45 to 928.55

(d) 859.3 to 940.7

(e) 824.00 to 927.06

29. The standard deviation of the test scores on a certain college placement test is known

to be 12.5. A random sample of 81 students had a mean score of 86.8. A 90%

confidence interval estimate for the average score of all students is

(a) 82.94 to 92.06

(b) 84.52 to 89.08

(c) 82.45 to 92.55

(d) 85.32 to 94.68

(e) 84.00 to 92.70

30. Which of the following statement is true for constructing the confidence interval

estimate for the population mean

(a) higher is the confidence interval, wider is the confidence interval for a fixed sample

size.

(b) larger is the sample standard deviation, wider is the confidence interval when the

sample size and confidence level are fixed

(c) in cases where the population standard deviation 0 is known, the appropriate

distribution to use to construct the interval is the normal distribution.

(d) In a confidence interval, the margin of error gets larger as the sample size is

increased.

(e) all of the above statements are true.

31. The average life of a sample of 30 car tires was found to be 60,000 miles. It is known

that the lifetimes of such tires are normally distributed with a standard deviation of

7,500 miles. A 95% confidence interval estimate of the mean life of all such tires was

calculated. The width of this confidence interval is

(a) 5937

(b) 5368

(c) 6357

(d) 5731

(e) 5846

32. The Nielsen Company reported that as of the third quarter of 2010, 28 percent of U.S.

mobile subscribers now have smart phones, cell phones with operating systems

resembling those of computers. The growing popularity of smart phones like Apple’s

iPhone, RIM’s Blackberry devices and a variety of Google Android-based models on the

market, has accelerated the adoption rate. Among those who acquired a new cell

phone in the past six months, 41 percent opted for a Smartphone over a standard

feature phone. A sample of 850 high school students was asked if they had a smart

phone. An overwhelming 578 indicated that they had a smart phone. The margin of

error at a 95% confidence would be

(a) 0.02

(b) 0.05

(c) 0.03

(d) 0.09

(e) 0.06

33. Approximately 51 percent of the U.S. population has at least two credit cards. (Source:

Experian national score index study, February 2007). Suppose a study of 500 consumers

showed that 315 carried three or more credit cards. A 95% confidence interval for the

proportion of U.S. population who carried three or more credit cards would be

(a) 0.588 to 0.734

(b) 0.598 to 0.689

(c) 0.633 to 0.732

(d) 0.588 to 0.672

(e) 0.355 to 0.896

34. The following expressions are for the confidence intervals for the mean:

1ooi(2.0)[ij

m and,

1ooi(2.0)[ij

Note that the difference between the two intervals is that the sample size in the second

interval is four times large compared to the first interval. What is the effect on the width

of the confidence interval of quadrupling the sample size while holding all the other

data fixed?

(a) increase the width of the confidence interval by 75%.

(b) increase the width of the confidence interval by one-half.

(c) decease the width of the confidence interval to one-third.

(d) leave the width ofthe confidence interval unchanged.

(e) reduce the width of the confidence interval by one one-half.

35. A quality engineer is interested in estimating the mean time required to assemble a bar

code scanner. If the engineer wishes to be 95% confident that the error in estimating

the mean time is less than 0.25 minutes, and she knows from the past experience that

the standard deviation of the assembly time is 0.75 minutes; the sample size she would

need is

(a) 20

(b) 24

(c) 25

(d) 35

(e) 30

36. The required sample size to estimate the mean for an a particular study resulted into

significantly large sample size. The analyst believes that he does not have the time or

the resources to collect such a large sample. Which of the following actions would lead

to a reduced sample size?

(a) the margin of error required in the actual study should be increased.

(b) the confidence level should be reduces.

(c) the variation in the population should be reduced.

(d) all of the above will lead to a reduced sample size.

37. A large hospital wants to estimate the mean time before the patients are attended

upon arrival to the hospital emergency room. From a past study, it is known that the

standard deviation of the waiting time is 12 minutes. If the hospital administration

wishes to estimate the mean time within 3 minutes with a 95% confidence, the sample

size needed will be

(a) 107

(b) 190

(c) 500

(d) 62

(e) 290

38. A manufacturer of plasma TVs has problems with excessive customer complaints and

consequent return of the product for repair or replacement. The quality control

department wants to determine the magnitude of the problem so that it can estimate

its warranty liability. The number of plasma TVs the quality engineer should sample

and inspect in order to estimate the fraction defective, p within 2% with a 95%

confidence would be

(a) 2500

(b) 2401

(c) 3000

(d) 2000

(e) 5300

39.A manufacturer of electronic chip is interested in estimating the fraction defective

chips produced in one of their plants. A random sample of 200 chips produced 12

defectives. The point estimate and a 95% confidence interval on the fraction defective

would be

(a) E ∶ 0.12 and 95% confidence interval 0.03 ≤ p ≤ 0.09

(b) E ∶ 0.06 and 95% confidence interval 0.03 ≤ p ≤ 0.09

(c) E ∶ 0.06 and 95% confidence interval 0.02 ≤ p ≤ 0.07

(d) E ∶ 0.06 and 95% confidence interval 0.06 ≤ p ≤ 0.09

(e) None ofthe above.

40. The poll conducted by media and other agencies use a 95% confidence unless specified

otherwise. A 95% confidence interval for p at a 95% confidence is given by

≨↲−⊨↕∙⊖⊖↿∣∟≼↕−⇪⋝

l’l

Where n is the sample size. Suppose}: 0.36 is the proportion of those in the sample

who approve of the way the President is handling the economy. If the margin of error is

$3 percent, the sample size used in the study was

(a) 735

(b) 840

(c) 984

(d) 649

(e) 526