INSTRUCTOR ANSWER GUIDE
OpenStax Introductory Business Statistics 2e
Instructor Answer Guide
,OpenStax Introductory Business Statistics 2e
Instructor Answer Guide
CHAPTER 9: HYPOTHESIS TESTING WITH ONE SAMPLE
Exercise 1. You are testing that the mean speed of your cable Internet connection is more than
three Megabits per second. What is the random variable? Describe in words.
Solution The random variable is the mean Internet speed in Megabits per second.
Exercise 2. You are testing that the mean speed of your cable Internet connection is more than
three Megabits per second. State the null and alternative hypotheses.
Solution H0: μ ≤ 3
Ha: μ > 3
Exercise 3. The American family has an average of two children. What is the random variable?
Describe in words.
Solution The random variable is the mean number of children an American family has.
Exercise 4. The mean entry level salary of an employee at a company is $58,000. You believe it is
higher for IT professionals in the company. State the null and alternative hypotheses.
Solution H0: μ = 58,000
Ha: μ > 58,000
Exercise 5. A sociologist claims the probability that a person picked at random in Times Square in
New York City is visiting the area is 0.83. You want to test to see if the proportion is
actually less. What is the random variable? Describe in words.
Solution The random variable is the proportion of people picked at random in Times Square
visiting the city.
Exercise 6. A sociologist claims the probability that a person picked at random in Times Square in
New York City is visiting the area is 0.83. You want to test to see if the claim is correct.
State the null and alternative hypotheses.
Solution H0: p = 0.83
Ha: p ≠ 0.83
Exercise 7. In a population of fish, approximately 42% are female. A test is conducted to see if, in
fact, the proportion is less. State the null and alternative hypotheses.
Solution H0: p = 0.42
Ha: p < 0.42
Exercise 8. Suppose that a previous study stated that the mean time spent in jail by a first–time
convicted burglar is 2.5 years. A revised study was then done to see if the mean time
has increased. A random sample of 26 first-time convicted burglars in a recent year
was picked. The mean length of time in jail from the survey was 3 years with a standard
2
October 28, 2025
, OpenStax Introductory Business Statistics 2e
Instructor Answer and Solution Guide
Chapter 9: Hypothesis Testing with One Sample
deviation of 1.8 years. Suppose that it is somehow known that the population standard
deviation is 1.5. If you were conducting a hypothesis test to determine if the mean
length of jail time has increased, what would the null and alternative hypotheses be?
The distribution of the population is normal.
State the null and alternative hypotheses.
a. H0: __________
b. Ha: __________
Solution a. H0: μ = 2.5 (or, H0: μ ≤ 2.5)
b. Ha : μ > 2.5
Exercise 9. A random survey of 75 people with student loans revealed that the mean length of time
in repayment is 17.4 years with a standard deviation of 6.3 years. If you were
conducting a hypothesis test to determine if the population mean time in repayment
could likely be 15 years, what would the null and alternative hypotheses be?
a. H0: __________
b. Ha: __________
Solution a. H0: μ = 15
b. Ha: μ ≠ 15
Exercise 10. The National Institute of Mental Health published an article stating that in any one-
year period, approximately 9.5% of American adults suffer from depression or a
depressive illness. Suppose that in a survey of 100 people in a certain town, seven of
them suffered from depression or a depressive illness. If you were conducting a
hypothesis test to determine if the true proportion of people in that town suffering from
depression or a depressive illness is lower than the percent in the general adult
American population, what would the null and alternative hypotheses be?
a. H0: __________
b. Ha: __________
Solution a. H0: p = 0.095
b. Ha: p < 0.095
Exercise 11. The mean price of mid-sized cars in a region is $32,000. A test is conducted to see if the
claim is true. State the Type I and Type II errors in complete sentences.
Solution Type I: The mean price of mid-sized cars is $32,000, but we conclude that it is not
$32,000. Type II: The mean price of mid-sized cars is not $32,000, but we conclude that
it is $32,000.
Exercise 12. A sleeping bag is tested to withstand temperatures of -15 °F. You think the bag cannot
stand temperatures that low. State the Type I and Type II errors in complete sentences.
Solution Type I: The bag can withstand -15 °F, but you conclude that it cannot stand
temperatures that low. Type II: The bag cannot withstand -15 °F, but you conclude that
it can.
3
October 28, 2025
OpenStax Introductory Business Statistics 2e
Instructor Answer Guide
,OpenStax Introductory Business Statistics 2e
Instructor Answer Guide
CHAPTER 9: HYPOTHESIS TESTING WITH ONE SAMPLE
Exercise 1. You are testing that the mean speed of your cable Internet connection is more than
three Megabits per second. What is the random variable? Describe in words.
Solution The random variable is the mean Internet speed in Megabits per second.
Exercise 2. You are testing that the mean speed of your cable Internet connection is more than
three Megabits per second. State the null and alternative hypotheses.
Solution H0: μ ≤ 3
Ha: μ > 3
Exercise 3. The American family has an average of two children. What is the random variable?
Describe in words.
Solution The random variable is the mean number of children an American family has.
Exercise 4. The mean entry level salary of an employee at a company is $58,000. You believe it is
higher for IT professionals in the company. State the null and alternative hypotheses.
Solution H0: μ = 58,000
Ha: μ > 58,000
Exercise 5. A sociologist claims the probability that a person picked at random in Times Square in
New York City is visiting the area is 0.83. You want to test to see if the proportion is
actually less. What is the random variable? Describe in words.
Solution The random variable is the proportion of people picked at random in Times Square
visiting the city.
Exercise 6. A sociologist claims the probability that a person picked at random in Times Square in
New York City is visiting the area is 0.83. You want to test to see if the claim is correct.
State the null and alternative hypotheses.
Solution H0: p = 0.83
Ha: p ≠ 0.83
Exercise 7. In a population of fish, approximately 42% are female. A test is conducted to see if, in
fact, the proportion is less. State the null and alternative hypotheses.
Solution H0: p = 0.42
Ha: p < 0.42
Exercise 8. Suppose that a previous study stated that the mean time spent in jail by a first–time
convicted burglar is 2.5 years. A revised study was then done to see if the mean time
has increased. A random sample of 26 first-time convicted burglars in a recent year
was picked. The mean length of time in jail from the survey was 3 years with a standard
2
October 28, 2025
, OpenStax Introductory Business Statistics 2e
Instructor Answer and Solution Guide
Chapter 9: Hypothesis Testing with One Sample
deviation of 1.8 years. Suppose that it is somehow known that the population standard
deviation is 1.5. If you were conducting a hypothesis test to determine if the mean
length of jail time has increased, what would the null and alternative hypotheses be?
The distribution of the population is normal.
State the null and alternative hypotheses.
a. H0: __________
b. Ha: __________
Solution a. H0: μ = 2.5 (or, H0: μ ≤ 2.5)
b. Ha : μ > 2.5
Exercise 9. A random survey of 75 people with student loans revealed that the mean length of time
in repayment is 17.4 years with a standard deviation of 6.3 years. If you were
conducting a hypothesis test to determine if the population mean time in repayment
could likely be 15 years, what would the null and alternative hypotheses be?
a. H0: __________
b. Ha: __________
Solution a. H0: μ = 15
b. Ha: μ ≠ 15
Exercise 10. The National Institute of Mental Health published an article stating that in any one-
year period, approximately 9.5% of American adults suffer from depression or a
depressive illness. Suppose that in a survey of 100 people in a certain town, seven of
them suffered from depression or a depressive illness. If you were conducting a
hypothesis test to determine if the true proportion of people in that town suffering from
depression or a depressive illness is lower than the percent in the general adult
American population, what would the null and alternative hypotheses be?
a. H0: __________
b. Ha: __________
Solution a. H0: p = 0.095
b. Ha: p < 0.095
Exercise 11. The mean price of mid-sized cars in a region is $32,000. A test is conducted to see if the
claim is true. State the Type I and Type II errors in complete sentences.
Solution Type I: The mean price of mid-sized cars is $32,000, but we conclude that it is not
$32,000. Type II: The mean price of mid-sized cars is not $32,000, but we conclude that
it is $32,000.
Exercise 12. A sleeping bag is tested to withstand temperatures of -15 °F. You think the bag cannot
stand temperatures that low. State the Type I and Type II errors in complete sentences.
Solution Type I: The bag can withstand -15 °F, but you conclude that it cannot stand
temperatures that low. Type II: The bag cannot withstand -15 °F, but you conclude that
it can.
3
October 28, 2025
