Question 1

College X is concerned about their employees making use of their email for non-business purposes. You have been approached to assist in this matter. College X decides on a 99% confidence level and state that the estimation proportion must be within 2 percent of the population proportion. A pilot survey reveals that 8 out of 50 emails sampled were not for business purposes. How many emails should be surveyed to meet your requirements?

Accepted Answer

A)  910 
B)  2,100 
C)  498 
D)  1,221 
E)  2,237

Question 2

What kind of distribution is the t distribution?

Accepted Answer

A)  Continuous 
B)  Discrete 
C)  Subjective 
D)  Standard

Question 3

i. The 95 percent confidence interval states that 95 percent of the sample means of a specified sample size selected from a population will lie within plus and minus 1.96 standard deviations of the hypothesized population mean. ii. A distribution of sample means is normally distributed with a mean equal to the population mean and a standard deviation equal to the standard error of the mean.
iii. A sample mean is the best point estimate of a population mean.

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 4

A survey of 144 retail stores revealed that the average price of a DVD was $375 with a standard error of $20. If 95% and 98% confidence intervals were developed to estimate the true cost of the DVD, what differences would they have?

Accepted Answer

A)  Standard errors 
B)  Interval widths 
C)  Z-values 
D)  Both standard errors and interval widths 
E)  Both interval widths and Z-values

Question 5

In order to construct a 95% confidence interval for the population mean when the population standard deviation is unknown and the sample size is 15, you should use the t-value indicated as:

Accepted Answer

A)  t0.10,15 
B)  t0.10,14 
C)  t0.05,15 
D)  t0.05,14 
E)  t0.025,14

Question 6

The following summarizes the amount of snowfall in Ontario over the past number of years.  You wonder whether the population mean could have been 1,600 or 2,100.

Accepted Answer

A)  Since 1600 is within the 95% confidence interval, the population mean is likely to be 1,600. 
B)  Since 1600 is not within the 95% confidence interval, the population mean is not likely to be 1,600. 
C)  Since 2100 is within the 95% confidence interval, the population mean is likely to be 2,100. 
D)  Since neither 1,600 nor 2,100 is within the 95% confidence interval, the population mean is not likely to be 1,600 or 2000. 
E)  Since 1900 and 2000 are both within the 95% confidence interval, the population mean is likely to be either value.

Question 7

The following summarizes the average price of Air Canada stock at the end of 20 randomly selected weeks in 2000.  Determine a 95% confidence interval for the average Air Canada stock price in 2000.

Accepted Answer

A)  [16.83, 17.42] 
B)  [14.90, 19.87] 
C)  [17.48, 19.40] 
D)  [16.24, 18.56] 
E)  [16.23, 18.55]

Question 8

College X is concerned about their employees making use of their email for non-business purposes. You have been approached to assist in this matter. College X decides on a 95% confidence level and state that the estimation proportion must be within 2 percent of the population proportion. A pilot survey reveals that 8 out of 50 emails sampled were not for business purposes. How many emails should be surveyed to meet your requirements?

Accepted Answer

A)  1,291 
B)  707 
C)  498 
D)  2,230 
E)  1,000

Question 9

College X is concerned about their employees making use of their email for non-business purposes. You have been approached to assist in this matter. College X decides on a 90% confidence level and state that the estimation proportion must be within 2 percent of the population proportion. A pilot survey reveals that 8 out of 50 emails sampled were not for business purposes. How many emails should be surveyed to meet your requirements?

Accepted Answer

A)  910 
B)  707 
C)  498 
D)  1,221 
E)  1,000

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:  The student from the course wonders whether the population mean could have been 75 or 80.

Accepted Answer

A)  Since 80 is within the 95% confidence interval, the population mean is likely to be 80. 
B)  Since 80 is not within the 95% confidence interval, the population mean is not likely to be 80. 
C)  Since 75 is within the 95% confidence interval, the population mean is likely to be 75. 
D)  Since neither 75 nor 80 is within the 95% confidence interval, the population mean is not likely to be 75 or 80. 
E)  Since 80 is not within the 95% confidence interval, the population mean is not likely to be 80, but it is likely to be 75.

Question 11

A random sample of 85 group leaders, supervisors, and similar personnel revealed that on the average a person spent 6.5 years on the job before being promoted. The standard deviation of the population was 1.7 years. Find the 95% confidence interval for the population mean.

Accepted Answer

A)  6.99 and 7.99 
B)  4.15 and 7.15 
C)  6.14 and 6.86 
D)  6.49 and 7.49

Question 12

The Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 25 people reveals the mean yearly consumption to be 27 kg with a sample standard deviation of 9 kg. Assume a normal population. Develop a 90% confidence interval for the mean annual consumption of sugar.

Accepted Answer

A)  23.06 to 30.94 
B)  23.285 to 30.715 
C)  21.97 to 32.03 
D)  23.30 to 30.70 
E)  23.92 to 30.08

Question 13

A random sample of 85 group leaders, supervisors, and similar personnel revealed that on the average a person spent 6.5 years on the job before being promoted. The standard deviation of the sample was 1.7 years. What is the 95% confidence interval for the true population mean?

Accepted Answer

A)  6.46 and 6.54 
B)  3.17 and 9.83 
C)  6.13 and 6.87 
D)  6.20 and 6.70 
E)  6.32 and 6.88

Question 14

A survey of an urban university (population of 25,450) showed that 870 of 1,100 students sampled supported a fee increase to fund improvements to the student recreation center. If university officials say that at least 70% of the voting student population support the fee increase, what conclusion can be drawn based on a 95% level of confidence?

Accepted Answer

A)  70% is not in the interval, need to take another sample. 
B)  70% is not in the interval, so assume it will not be supported. 
C)  70% is below the interval, so assume it will be supported. 
D)  Since this was not based on population, cannot make conclusion.

Question 15

College X is concerned about their employees making use of their email for non-business purposes. A random sample of 400 e-mails discovered 60 messages that were not business related. The 95% confidence interval for the population proportion is:

Accepted Answer

A)  0.104 to 0.196 
B)  0.115 to 0.185 
C)  0.148 to 0.252 
D)  0.121 to 0.179 
E)  0.186 to 0.254

Question 16

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

Question 17

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 18

The following summarizes the average price of Air Canada stock at the end of 20 randomly selected weeks in 2000.  Determine a 98% confidence interval for the average TSE 300 stock index in 2000.

Accepted Answer

A)  [9467.57, 10 084.68] 
B)  [9401.80, 10 150.40] 
C)  [9628.70, 9923.55] 
D)  [9468.61, 10 083.65]

Question 19

A survey of 144 retail stores revealed that the average price of a DVD was $375 with a standard error of $20. If 90% and 95% confidence intervals were developed to estimate the true cost of the DVD, what similarities would they have?

Accepted Answer

A)  Point estimates 
B)  Z-values would be the same 
C)  Standard errors 
D)  Both point estimates and standard errors would be the same 
E)  Both standard errors Z-values would be the same

Question 20

The Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 25 people reveals the mean yearly consumption to be 27 kg with a sample standard deviation of 9 kg. Assume a normal population. For a 95% confidence interval, what is the critical value needed?

Accepted Answer

A)  t = 2.787 
B)  t = 2.064 
C)  t = 2.797 
D)  z = 1.645 
E)  z = 1.96

Exam 8: Estimation and Confidence Intervals