Question 1

Recently, a university surveyed recent graduates of the English Department for their starting
Salaries. One hundred graduates returned the survey. The average salary was $35,000 with a
Standard deviation of $2,000.
What is the best point estimate of the population mean?

Accepted Answer

A)  $25,000 
B)  $2,000 
C)  $500 
D)  $400 
E)  $35,000

Question 2

Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile
Tires. The average tread life was found to be 80,000 kilometres with a standard deviation of 5,600
Kilometres. What is the best estimate of the average tread life in miles for the entire population of
These tires?

Accepted Answer

A)  80,000 
B)  5,600 
C)  (80,000/100) 
D)  (5,600/100)

Question 3

The mean number of travel days per year for the outside salespeople employed by hardware
Distributors is to be estimated. The 0.90 degree of conﬁdence is to be used. The mean of a small
Pilot study was 150 days, with a standard deviation of 14 days. If the population mean is to be
Estimated within two days, how many outside salespeople should be sampled?

Accepted Answer

A)  133 
B)  452 
C)  511 
D)  2,100

Question 4

A sample of 20 is selected from the population. What is the number of degrees of freedom used to
Determine the appropriate critical t-value?

Accepted Answer

A)  20 
B)  19 
C)  21 
D)  25

Question 5

Dr. Patton is a professor of English. Recently she counted the number of misspelled works in a
Group of student essays. She noted the distribution of misspelled words per essay followed the
Normal distribution with a standard deviation of 2.44 words per essay. For her Tuesday class of 44
Students, the mean number of misspelled words per essay was 6.05. Construct a 90% conﬁdence
Interval for the mean number of misspelled words in the population of student essays.

Accepted Answer

A)  5.374 to 6.726 
B)  5.161 to 6.939 
C)  5.102 to 6.998 
D)  5.482 to 6.618 
E)  5.445 to 6.6551

Question 6

i. The higher the degree of conﬁdence, the larger the sample required to give a certain precision.
ii. To determine the size of a sample, the standard deviation of the population must be estimated by
Either taking a pilot survey or by approximating it based on knowledge of the population.
iii. One factor in determining the size of a sample is the maximum allowable error that you must
Decide on. It is the maximum error you will tolerate at a speciﬁed level of conﬁdence.

Accepted Answer

A)  (i), (ii), and (iii) are all correct statements. 
B)  (iii) is a correct statement but not (i) or (ii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements.

Question 7

A group of statistics students decided to conduct a survey at their university to ﬁnd the average
(mean) amount of time students spent studying per week. Assuming a standard deviation of 3
Hours, what is the required sample size if the error is to be less than ½ hour with a 99% level of
Conﬁdence?

Accepted Answer

A)  196 
B)  240 
C)  15 
D)  16

Question 8

(i. The interval estimate states the range within which a population parameter probably lies.
(ii. A 95 percent conﬁdence interval implies that about 95 out of 100 similarly constructed intervals
Will include the parameter being estimated.
(iii) For a sampling distribution of the means, 95% percent of the means would be between ± 1.96
Standard deviations.

Accepted Answer

A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements.

Question 9

The following summarizes the amount of snowfall in Ontario over the past number of years.  If 90% and 95% conﬁdence intervals were developed to estimate the true average annual snowfall,
What similarities would they have?

Accepted Answer

A)  Point estimates 
B)  Z-values 
C)  Standard errors 
D)  Both point estimates and standard errors 
E)  Both point estimates and Z-Values

Question 10

A statistics professor wishes to estimate the average mark on a term test for a course that has
Multiple sections and many students. A survey of some of the students registered for the course
Reveals the following results: 
Determine a 95% conﬁdence interval for the term test results.

Accepted Answer

A)  [48.0, 93.6] 
B)  [66.8, 74.8] 
C)  [62.9, 78.71] 
D)  [64.2, 77.3] 
E)  [62.6, 79.0]

Question 11

i. The test statistic for a problem involving an unknown population standard deviation is the
Student's t distribution.
ii. The t distribution approaches the Z distribution as the sample size increases.
iii. As the sample size increases, the computed value of t decreases.

Accepted Answer

A)  (i), (ii), and (iii) are all correct statements. 
B)  (iii) is a correct statement but not (i) or (ii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements.

Question 12

(i. The interval estimate states the range within which a population parameter probably lies.
(ii. The conﬁdence interval is the interval within which a population parameter is expected to lie.
(iii) For a sampling distribution of the means, 95% percent of the means would be between ± 1.96
Standard deviations.

Accepted Answer

A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements.

Question 13

Suppose 1,600 of 2,000 registered voters sampled said they planned to vote for a particular
Candidate. Using the 0.95 degree of conﬁdence, what is the interval estimate for the population
Proportion (to the nearest tenth of a percent)?

Accepted Answer

A)  78.2% to 81.8% 
B)  69.2% to 86.4% 
C)  76.5% to 83.5% 
D)  77.7% to 82.3%

Question 14

Dr. Patton is a professor of English. Recently she counted the number of misspelled works in a
Group of student essays. She noted the distribution of misspelled words per essay followed the
Normal distribution with a standard deviation of 2.44 words per essay. For her Tuesday class of 50
Students, the mean number of misspelled words per essay was 6.05. Construct a 90% conﬁdence
Interval for the mean number of misspelled words in the population of student essays.

Accepted Answer

A)  5.374 to 6.726 
B)  5.161 to 6.939 
C)  5.102 to 6.998 
D)  5.482 to 6.618 
E)  5.445 to 6.3655

Question 15

A sample of 50 is selected from a known population of 250 elements. The population standard
Deviation is 15. What is the standard error of the sample means using the ﬁnite population
Correction factor?

Accepted Answer

A)  2.89 
B)  1.90 
C)  2.12 
D)  13.44 
E)  Cannot be determined from information given.

Question 16

A manager of a local store wants to estimate the mean amount spent per shopping visit by
Customers. Summary statistics from a sample taken reveal the following: 
The store manager wonders whether the population mean could have been $50 or $60.

Accepted Answer

A)  Since $60 is within the 95% conﬁdence interval, the population mean is likely to be $60. 
B)  Since $60 is not within the 95% conﬁdence interval, the population mean is not likely to be $60. 
C)  Since $50 is within the 95% conﬁdence interval, the population mean is likely to be $50. 
D)  Since $50 is not within the 95% conﬁdence interval, the population mean is not likely to be $50. 
E)  Since $60 is not within the 95% conﬁdence interval, the population mean is not likely to be $60; however, it is likely to be $50.

Question 17

Which statement(s) is/are correct about the t distribution?

Accepted Answer

A)  Mean = 0 
B)  Symmetric 
C)  Based on degrees of freedom 
D)  Mean = 0, symmetric and based on degrees of freedom 
E)  Mean = 0 and symmetric

Question 18

Recently, a university surveyed recent graduates of the English Department for their starting
Salaries. Four hundred graduates returned the survey. The average salary was $55,000. The
Population standard deviation is known to be $2,500.
What is the 90% conﬁdence interval for the mean salary of all graduates from the English
Department?

Accepted Answer

A)  5,497, $55,039 
B)  54,794, $55,206 
C)  54,671, $55,329 
D)  54,961, $5,539 
E)  54,800, $55,200

Question 19

The t distribution is similar to the z distribution in all BUT ONE of the following characteristics. Which
One is it?

Accepted Answer

A)  Continuous 
B)  Symmetrical 
C)  Bell-shaped 
D)  t distribution's mean = 0 and standard deviation = 1

Question 20

A survey of 25 grocery stores revealed that the average price of a 4-litre bag of milk was $2.98 with
A standard error of $0.10. What is the 98% conﬁdence interval to estimate the true cost of a 4-litre
Bag of milk?

Accepted Answer

A)  $2.75 to $3.21 
B)  $2.85 to $3.11 
C)  $2.94 to $3.02 
D)  $2.95 to $3.01 
E)  $2.77 to $3.19

Exam 8: Sampling Methods and the Central Umit Theorem

Recently, a university surveyed recent graduates of the English Department for their starting Salaries. One hundred graduates returned the survey. The average salary was $35,000 with a Standard deviation of $2,000. What is the best point estimate of the population mean?

A sample of 20 is selected from the population. What is the number of degrees of freedom used to Determine the appropriate critical t-value?

The following summarizes the amount of snowfall in Ontario over the past number of years. If 90% and 95% conﬁdence intervals were developed to estimate the true average annual snowfall, What similarities would they have?

A statistics professor wishes to estimate the average mark on a term test for a course that has Multiple sections and many students. A survey of some of the students registered for the course Reveals the following results: Determine a 95% conﬁdence interval for the term test results.

i. The test statistic for a problem involving an unknown population standard deviation is the Student's t distribution. ii. The t distribution approaches the Z distribution as the sample size increases. iii. As the sample size increases, the computed value of t decreases.

Suppose 1,600 of 2,000 registered voters sampled said they planned to vote for a particular Candidate. Using the 0.95 degree of conﬁdence, what is the interval estimate for the population Proportion (to the nearest tenth of a percent) ?

A sample of 50 is selected from a known population of 250 elements. The population standard Deviation is 15. What is the standard error of the sample means using the ﬁnite population Correction factor?

A manager of a local store wants to estimate the mean amount spent per shopping visit by Customers. Summary statistics from a sample taken reveal the following: The store manager wonders whether the population mean could have been $50 or $60.

Which statement(s) is/are correct about the t distribution?

The t distribution is similar to the z distribution in all BUT ONE of the following characteristics. Which One is it?

A survey of 25 grocery stores revealed that the average price of a 4-litre bag of milk was $2.98 with A standard error of $0.10. What is the 98% conﬁdence interval to estimate the true cost of a 4-litre Bag of milk?