ECON1005 Final Exam Review Packet
The following concepts can be tested on the Final Exam. Use the following check list and the review problems
to help you in your studying.
This packet is not meant to be a comprehensive review packet, but it is to be used along with your class notes,
problem sets and chapter readings. This packet is created to assist you in your review. It only illustrates the
types of questions that may come on the exam. The answer key is provided in a separate file. It is for review
only and is no reflection of the number of questions that will be on the exam. Irrespectively of the number of
questions, the mid semester exam can be completed in an hour or less.
Note that although the test is limited to the topics listed in the table below and being MCQs, there are a myriad
of ways to present such questions. Again, you are strongly encouraged to practice the questions completed in
lectures and all the questions on the tutorial sheets (tutorial questions + extra questions).
Concept
Population vs. sample
Parameter vs. statistic
Types of sampling methods (including identifying sampling methods used in given scenarios)
Experiments vs. observations vs. anecdotal evidence
Types of data/variables:
 Quantitative vs. categorical
 Primary vs. secondary
 Discrete vs. continuous
Levels of Measurement
Types of graphs (identifying the best graph to use in given scenarios)
 Bar graph
 Pie chart
 Stem & leaf (including back-to-back stem & leaf)
 Histogram
 Cumulative Ogive (less than and more than; including using the graphs to obtain
estimates)
 Boxplots (including side-by-side boxplot; identifying shape)
Numerical methods for describing data - selecting the best method given a scenario
 Measures of shape (skewness and number of peaks)
 Measures of central tendency (mode, median, mean, weighted mean)
 Measures of variability (range, variance, standard deviation, IQR)
 5-number summary (minimum, Q1, median, Q3, maximum)
Sampling distributions and central limit theorem (including differentiating between a
probability distribution and a sampling distribution question)
Reviewed
ECON1005: Introductory Statistics
Final Exam Review Packet
Concept
Reviewed
Inference for means (sampling distributions, confidence intervals, sample size calculation,
hypothesis testing)
Inference for proportions (sampling distributions, confidence intervals, sample size calculation,
hypothesis testing)
When to use a hypothesis test over a confidence interval and vice versa
Below are the critical values (z*) for the Normal distribution.
Confidence Level
80%
90%
95%
99%
99.5%
Z*
1.282
1.645
1.960
2.576
2.807
USE THE FOLLOWING TO ANSWER QUESTIONS 1 – 4: Match each of the following with the SINGLE
choice that best describes the given situation. Each answer choice may be used once, more than once, or not at
all.
A. Simple random sample
D. Voluntary response
B. Stratified random sample
E. Cluster sample
C. Multistage random sample
1. There are thirty tutorial sections of an introductory statistics class. A random sample of three sections is
chosen, and then random samples of 8 students from each selected section are chosen to participate in a
survey.
2. A farmer is interested in studying the beef production from his cows. He has three types of beef producing
cows: Jamaica Black, Jamaica Red Poll and Jamaica Brahman. He takes a random sample of cows from
each type and measures their beef production at the time of slaughter.
3. How long does the average commercial break last on the network television stations? On eight randomly
selected days of the month, 5 time slots are randomly chosen and one show is randomly selected from each
time slot. The length of each commercial during this time is recorded, and the average determined.
4. An introductory psychology lecturer is interested in how the lectures are going this semester for her classes.
She asks students to send her feedback on the lectures by email. Some of the students respond, and she
records the number of positive and negative responses from these emails.
USE THE FOLLOWING TO ANSWER QUESTIONS 5 – 7: A fertilizer company wants to know the
average number of acres of sugar cane grown per farm in Jamaica. They divide all farms into four classes
depending on their size. From each class, they select a sample of 5 farms and count and record the number of
acres of sugar cane on each selected farm
.
5. Which of the following represents the population for this study?
a)
b)
c)
d)
e)
All farms in Jamaica.
The 60 selected farms.
The 4 classes of farms.
The 15 selected farms.
You are unable to determine the sample from the information given.
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ECON1005: Introductory Statistics
Final Exam Review Packet
6. The response variable for this problem is
a)
b)
c)
d)
e)
A farm in Jamaica.
The average size of farms in Jamaica.
The size of a selected farm in Jamaica.
The average number of acres of sugar cane grown per farm in Jamaica.
The number of acres of sugar cane grown on a selected farm in Jamaica.
7. What type of sampling design was used in this study?
a)
b)
c)
d)
e)
A simple random sample.
A stratified random sample.
A multistage random sample.
A cluster sample.
A voluntary response sample.
USE THE FOLLOWING TO ANSWER QUESTIONS 8-11: Indicate the letter corresponding to the type of
graph that would be best for the following situations. Each answer choice may be used once, more than once,
or not at all.
A. Histogram
B. Side-by-Side Boxplot
C. Bar Graph
D. Pie Chart
E. Stemplot
8. We want to plot the distribution of the amount of soda consumed per week by 100 adults who volunteered
to participate in certain study.
9. We ask students the reason they were late to class. Students may give more than one response.
10. A lecture wants to compare the scores on an exam based on faculty the student is in.
11. A researcher wants to display the per capita GDP for the 15 full members of CARICOM.
USE THE FOLLOWING INFORMATION TO ANSWER QUESTIONS 12 &13: A certain brand of bean
is made so that each package contains about the same number of beans. The filling procedure is not perfect
however. The packages are filled with an average of 375 beans, which is normally distributed with a standard
deviation of 8. Yesterday Kaydian went to the store and purchased 4 of these packages. Out of curiosity, she
counted the number of beans in these packages – her four bags contained an average of 382 beans.
12. In the above scenario, which of the following is a parameter?
a)
b)
c)
d)
The average number of beans in Kaydian’s packages – 382
The average number of beans in Kaydian’s packages – which is unknown.
The average number of beans in all packages made – 375
The average number of beans in all packages made – which is unknown.
13. If you went to the store and purchased six bags of this brand of bean, what is the probability that the
average number of beans in your bags is less than 373?
a)
b)
c)
d)
0.2709
0.3085
0.4013
0.7291
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ECON1005: Introductory Statistics
Final Exam Review Packet
14. Random samples of size n were selected from a population with a known standard deviation. How is the
standard deviation of the sampling distribution of the sample mean affected if the sample size is increased
from 50 to 200?
a)
b)
c)
d)
It remains the same.
It is multiplied by four.
It is divided by four.
It is divided by two
15. Let X be a random variable that has a bimodal distribution with mean 12 and standard deviation 1.5. Based
on random samples of size 400, the sampling distribution of the mean is
a)
b)
c)
d)
highly skewed with mean 12 and standard deviation 1.5
slightly bimodal with mean 12 and standard deviation 1.5
approximately normal with mean 12 and standard deviation 0.00375
approximately normal with mean 12 and standard deviation 0.075
16. Which of the following statements best describes the relationship between a parameter and a statistic?
a) A parameter has a sampling distribution with the statistic as its mean.
b) A parameter has a sampling distribution that can be used to determine what values the statistic
is likely to have in repeated samples.
c) A parameter is used to estimate a statistic.
d) A statistic is used to estimate a parameter.
17. A randomly selected sample of 400 students at a university with 15-week semesters was asked whether or
not they think the semester should be shortened to 14 weeks (with longer classes). Forty-six percent (46%)
of the 400 students surveyed answered "yes." Which one of the following statements about the number 46%
is correct?
a)
b)
c)
d)
It is a sample statistic.
It is a population parameter.
It is a margin of error.
It is a standard error.
18. A hypothesis test is conducted and the p-value of the test statistic is 0.02. Four of the following statements
are valid. Which statement is not valid?
a) It is not very likely that the extremeness of the test statistic is due to chance.
b) Assuming the null hypothesis is true, there is a 2% chance of getting a more extreme test
statistic.
c) There is a 2% chance that the null hypothesis is false.
d) At the 0.05 significance level, you would reject the null hypothesis.
e) At the 0.01 significance level, you would fail to reject the null hypothesis.
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ECON1005: Introductory Statistics
Final Exam Review Packet
19. Suppose that at the 95% confidence level we calculate a confidence interval described by 43.8 < µ < 46.2.
Which of the following statements cannot be made about this result.
a) The sample mean is 45.
b) The population mean is 45.
c) The margin of error is 1.2.
d) We are 95% confident that the population mean lies between 43.8 and 46.2.
20. You test a claim that more than 10% of adults have tattoos. Your test statistic turns out to be z = 2.31.
What is the p-value of this test statistic?
a)
b)
c)
d)
0.9896
0.0104
0.0208
0.0951
21. A random sample of 450 vacationers in a huge luxury resort showed that 150 were business executives. We
want to create a 95% confidence interval for the proportions of vacationers who are business executives.
a) What is the value at the centre of the 95% confidence interval? Write the symbol and value.
b) What is the critical value for this confidence interval? Write both the letter and value corresponding to
this interval.
c) What is the margin of error for this interval? Write (i) the formula, (ii) substitute the values and (iii) do
the calculations for this interval.
d) What is the 95% confidence interval for this data?
Lower limit = _________________________
Upper limit = _________________________
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ECON1005: Introductory Statistics
Final Exam Review Packet
e) This confidence interval applies to the (circle one of the options below):
sample
population
22. If a machine produces 5% defective jobs, it needs to be realigned. A random sample of 400 jobs revealed
that 28 are defective. Test at the 1% level of significance whether or not the machine needs to be realigned.
a) Write down the null and alternative hypothesis. Make sure to use the correct notation and definitions.
b) Calculate the test statistic. Write the equation for calculating the test statistic (including the letter) and
then substitute the necessary values. Write your answer to 3 decimal places.
c) Write the probability statement of the p-value in terms of the test statistic. First, write the general
formula and then substitute the necessary value. Also calculate the p-value.
d) If the curve below corresponds to the density curve of the test statistic, indicate the value at the centre,
indicate the location of the test statistic for this problem and shade and label the area corresponding to
the p-value.
e) Write the conclusion for this hypothesis test in terms of the problem. Be sure to state whether the
conclusion applies to the population or the sample.
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ECON1005: Introductory Statistics
Final Exam Review Packet
23. Bags of a certain brand of chips claim to have a net weight of 14 ounces but the net weight varies slightly
from bag to bag, with a population standard deviation of 0.24. A representative of a consumer advocacy
group wishes to see if there is any evidence that the mean net weight is less than advertised. A sample of
16 bags of this brand of chips is found to have a net weight of 13.82. Use these data to perform an
appropriate test of hypothesis at 5% significance level.
a) Write down the null and alternative hypothesis. Make sure to use the correct notation and definitions.
b) Calculate the test statistic. Write the equation for calculating the test statistic (including the letter) and
then substitute the necessary values. Write your answer to 3 decimal places.
c) Write the probability statement of the p-value in terms of the test statistic. First, write the general
formula and then substitute the necessary value. Also calculate the p-value.
d) If the curve below corresponds to the density curve of the sampling distribution of the mean, indicate
the value at the centre, indicate the location of the sample value for this problem and shade and label
the area corresponding to the p-value.
e) Write the conclusion for this hypothesis test in terms of the problem. Be sure to state whether the
conclusion applies to the population or the sample.
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ECON1005: Introductory Statistics
Final Exam Review Packet
24. The balances of all savings accounts at a local bank have a distribution that is skewed to the right with its
mean equal to $12,450 and standard deviation equal to $4,300. Find the probability that the mean balance
of a sample of 50 savings accounts selected from this bank will be more than $11,500.
a) Write down the probability statement to calculate the probability of interest. Make sure to use the
correct notation. (3 marks)
b) Calculate the z-score needed to calculate the probability of interest. Write the formula used to calculate
the z-score, substitute the necessary values. Write the final answer to two decimal places. (4 marks)
c) Calculate the probability of interest. Marks will only be given where all workings are shown. (4 marks)
d) Below is a density curve corresponding to the Standard Normal Distribution. Using the information
calculated above, fill in the values corresponding to the empty boxes. (4 marks)
1. The value at the centre of the distribution
2. The z-score
3. The probability corresponding to the shaded area
3.
2.
1.
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ECON1005: Introductory Statistics
Final Exam Review Packet
e) Below is a density curve corresponding to the Sampling Distribution of the Mean. Using the
information calculated above, fill in the values corresponding to the empty boxes. (4 marks)
1. The value at the centre of the distribution
2. The average
3. The probability corresponding to the shaded area
3.
2.
1.
25. A mail-order firm promises its customers that the products ordered will be mailed wining 72 hours of the
order being placed. The quality control department of the firm checks periodically to determine if the
promise is kept. Recently the quality control department took a sample of 50 orders and found that 35 of
them were mailed within 72 hours of the placement of the order. They want to create a 99% confidence
interval for the percentage of all orders that are mailed within 72 hours of their placement.
a) What is the value at the centre of the 99% confidence interval? Write the symbol and value.
b) What is the critical value for this confidence interval? Write both the letter and value corresponding to
this interval.
c) What is the margin of error for this interval? Write (i) the formula, (ii) substitute the values and (iii) do
the calculations for this interval.
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ECON1005: Introductory Statistics
Final Exam Review Packet
d) What is the 99% confidence interval for this data?
Lower limit = _________________________
Upper limit = _________________________
e) This confidence interval applies to the (circle one of the options below):
sample
population
26. According to official government data, the average annual expenditure on health care in a small Caribbean
island is $3,650 per person. The standard deviation for the population is known to be $1,460. A random
sample of 210 persons showed that they spent an average of $3,850 on health care last year. Test at the 2%
level of significance if there has been an increase in the annual health expenditure for all the persons in the
island.
a) Write down the null and alternative hypothesis. Make sure to use the correct notation and definitions.
b) Calculate the test statistic. Write the equation for calculating the test statistic (including the letter) and
then substitute the necessary values. Write your answer to 3 decimal places.
c) Write the probability statement of the p-value in terms of the test statistic. First, write the general
formula and then substitute the necessary value. Also calculate the p-value.
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ECON1005: Introductory Statistics
Final Exam Review Packet
d) If the curve below corresponds to the density curve of the sampling distribution of the mean, indicate
the value at the centre, indicate the location of the sample value for this problem and shade and label
the area corresponding to the p-value.
e) Write the conclusion for this hypothesis test in terms of the problem. Be sure to state whether the
conclusion applies to the population or the sample.
27. There has been an increase in the number of persons who are abandoning brand-name products and buying
store-brand products to save money. The marketing manager of a company that produces brand-name
coffee claims that 40% of persons prefer to by brand-name coffee. A random sample of 700 people who
buy coffee showed that 250 of them buy brand-name coffee. Using the 1% level of significance, can you
conclude that the percentage of people who buy brand-name coffee is different from the marketing
manager’s claim?
a) Write down the null and alternative hypothesis. Make sure to use the correct notation and definitions.
b) Calculate the test statistic. Write the equation for calculating the test statistic (including the letter) and
then substitute the necessary values. Write your answer to 3 decimal places.
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ECON1005: Introductory Statistics
Final Exam Review Packet
c) Write the probability statement of the p-value in terms of the test statistic. First, write the general
formula and then substitute the necessary value. Also calculate the p-value.
d) If the curve below corresponds to the density curve of the sampling distribution of the proportion,
indicate the value at the centre, indicate the location of the sample value for this problem and shade and
label the area corresponding to the p-value.
e) Write the conclusion for this hypothesis test in terms of the problem. Be sure to state whether the
conclusion applies to the population or the sample.
28. According to the US Census Bureau's American Community Survey, 87 percent of Americans over the age
of 25 have earned a high school diploma. Suppose we are going to take a random sample of 200 Americans
in this age group and calculate what proportion of the sample has a high school diploma. What is the
probability that the proportion of people in the sample with a high school diploma is less than 85 percent?
a) Write down the probability statement to calculate the probability of interest. Make sure to use the
correct notation. (3 marks)
b) Calculate the z-score needed to calculate the probability of interest. Write the formula used to calculate
the z-score, substitute the necessary values. Write the final answer to two decimal places. (4 marks)
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ECON1005: Introductory Statistics
Final Exam Review Packet
c) Calculate the probability of interest. Marks will only be given where all workings are shown. (4 marks)
d) Below is a density curve corresponding to the Standard Normal Distribution. Using the information
calculated above, fill in the values corresponding to the empty boxes. (4 marks)
4. The value at the centre of the distribution
5. The z-score
6. The probability corresponding to the shaded area
3.
2.
1.
e) Below is a density curve corresponding to the Sampling Distribution of the Proportion. Using the
information calculated above, fill in the values corresponding to the empty boxes. (4 marks)
1. The value at the centre of the distribution
2. The proportion
3. The probability corresponding to the shaded area
3.
2.
1.
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