STAT 2023 MODULE 4 TEST 2026 COMPLETE
STATISTICS PROBLEMS AND CORRECT
ANSWERS FULL REVIEW
◉ A university interested in tracking its honors program believes
that the proportion of graduates with a GPA of 3.00 or below is less
than 0.20. In a sample of 200 graduates, 30 students have a GPA of
3.00 or below. In testing the university's belief, how does one define
the population parameter of interest? Answer: It's the proportion of
honors graduates with a GPA of 3.00 or below.
The parameter to be tested is the population proportion of honors
graduates.
◉ The Institute of Education Sciences measures the high school
dropout rate as the percentage of 16-through 24-year-olds who are
not enrolled in school and have not earned a high school credential.
In 2009, the high school dropout rate was 8.1%. A polling company
recently took a survey of 1,000 people between the ages of 16 and
24 and found that 6.5% of them are high school dropouts. The
polling company would like to determine whether the dropout rate
has decreased. When testing whether the dropout rate has
decreased, the appropriate hypotheses are _____________ Answer: Ho:
p greater than or equal to 0.081, Ha: p <0.081
,The competing hypotheses are Ho: p ≥ po,HA: < po. It is referred to
as a left-tailed test of the population proportion.
◉ What type of data would necessitate using a hypothesis test of the
population proportion rather than a test of the population mean?
Answer: Qualitative
The population proportion p is the essential descriptive measure
when the data type is qualitative.
◉ The owner of a large car dealership believes that the financial
crisis decreased the number of customers visiting her dealership.
The dealership has historically had 800 customers per day. The
owner takes a sample of 100 days and finds the average number of
customers visiting the dealership per day was 750. Assume that the
population standard deviation is 350. The population parameter to
be tested is ___________. Answer: the mean number of customers
visiting the dealership per day
The parameter to be tested is the mean number of customers
visiting the dealership per day.
,◉ If the chosen significance level is α = 0.05, then
____________________________________________. Answer: there is a 5%
probability of rejecting a true null hypothesis
The significance level is the probability of committing a Type I error,
which is the probability of rejecting the null hypothesis when the
null hypothesis is true.
◉ Vermont-based Green Mountain Coffee Roasters dominates the
market for single-serve coffee in the United States, with its
subsidiary Keurig accounting for approximately 70% of sales
("Rivals Try to Loosen Keurig's Grip on Single-Serve Coffee Market,"
Chicago Tribune, February 26, 2011). But Keurig's patent on K-cups,
the plastic pods used to brew the coffee, is expected to expire in
2012, allowing other companies to better compete. Suppose a
potential competitor has been conducting blind taste tests on its
blend and finds that 47% of consumers strongly prefer its French
Roast to that of Green Mountain Coffee Roasters. After tweaking its
recipe, the competitor conducts a test with 144 tasters, of which 72
prefer its blend. The competitor claims that its new blend is
preferred by more than 47% of consumers to Green Mountain Coffee
Roasters' French Roast. Which of the following should be used to
develop the null and alte Answer: p is less than or equal to 0.47, Ha:
p>0.47
, The competing hypotheses are Ho: p ≥ po,HA: < po. It is referred to
as a left-tailed test of the population proportion.
◉ When we reject the null hypothesis when it is actually false, we
have committed _________. Answer: no error
◉ What is the decision rule when using the p-value approach to
hypothesis testing? Answer: Reject Ho if the p-value < α.
The decision rule is to reject the null hypothesis if the p-value < α
and not reject the null hypothesis if the p-value ≥ α.
◉ On the basis of sample information, we either "accept the null
hypothesis" or "reject the null hypothesis."
True Answer: False
On the basis of sample information, we either "reject the null
hypothesis" or "do not reject the null hypothesis." Only one of two
hypotheses is true and the hypotheses cover all possible values of
the population parameter.
◉ What is the decision rule when using the p-value approach to
hypothesis testing? Answer: Reject Ho if the p-value < α.
STATISTICS PROBLEMS AND CORRECT
ANSWERS FULL REVIEW
◉ A university interested in tracking its honors program believes
that the proportion of graduates with a GPA of 3.00 or below is less
than 0.20. In a sample of 200 graduates, 30 students have a GPA of
3.00 or below. In testing the university's belief, how does one define
the population parameter of interest? Answer: It's the proportion of
honors graduates with a GPA of 3.00 or below.
The parameter to be tested is the population proportion of honors
graduates.
◉ The Institute of Education Sciences measures the high school
dropout rate as the percentage of 16-through 24-year-olds who are
not enrolled in school and have not earned a high school credential.
In 2009, the high school dropout rate was 8.1%. A polling company
recently took a survey of 1,000 people between the ages of 16 and
24 and found that 6.5% of them are high school dropouts. The
polling company would like to determine whether the dropout rate
has decreased. When testing whether the dropout rate has
decreased, the appropriate hypotheses are _____________ Answer: Ho:
p greater than or equal to 0.081, Ha: p <0.081
,The competing hypotheses are Ho: p ≥ po,HA: < po. It is referred to
as a left-tailed test of the population proportion.
◉ What type of data would necessitate using a hypothesis test of the
population proportion rather than a test of the population mean?
Answer: Qualitative
The population proportion p is the essential descriptive measure
when the data type is qualitative.
◉ The owner of a large car dealership believes that the financial
crisis decreased the number of customers visiting her dealership.
The dealership has historically had 800 customers per day. The
owner takes a sample of 100 days and finds the average number of
customers visiting the dealership per day was 750. Assume that the
population standard deviation is 350. The population parameter to
be tested is ___________. Answer: the mean number of customers
visiting the dealership per day
The parameter to be tested is the mean number of customers
visiting the dealership per day.
,◉ If the chosen significance level is α = 0.05, then
____________________________________________. Answer: there is a 5%
probability of rejecting a true null hypothesis
The significance level is the probability of committing a Type I error,
which is the probability of rejecting the null hypothesis when the
null hypothesis is true.
◉ Vermont-based Green Mountain Coffee Roasters dominates the
market for single-serve coffee in the United States, with its
subsidiary Keurig accounting for approximately 70% of sales
("Rivals Try to Loosen Keurig's Grip on Single-Serve Coffee Market,"
Chicago Tribune, February 26, 2011). But Keurig's patent on K-cups,
the plastic pods used to brew the coffee, is expected to expire in
2012, allowing other companies to better compete. Suppose a
potential competitor has been conducting blind taste tests on its
blend and finds that 47% of consumers strongly prefer its French
Roast to that of Green Mountain Coffee Roasters. After tweaking its
recipe, the competitor conducts a test with 144 tasters, of which 72
prefer its blend. The competitor claims that its new blend is
preferred by more than 47% of consumers to Green Mountain Coffee
Roasters' French Roast. Which of the following should be used to
develop the null and alte Answer: p is less than or equal to 0.47, Ha:
p>0.47
, The competing hypotheses are Ho: p ≥ po,HA: < po. It is referred to
as a left-tailed test of the population proportion.
◉ When we reject the null hypothesis when it is actually false, we
have committed _________. Answer: no error
◉ What is the decision rule when using the p-value approach to
hypothesis testing? Answer: Reject Ho if the p-value < α.
The decision rule is to reject the null hypothesis if the p-value < α
and not reject the null hypothesis if the p-value ≥ α.
◉ On the basis of sample information, we either "accept the null
hypothesis" or "reject the null hypothesis."
True Answer: False
On the basis of sample information, we either "reject the null
hypothesis" or "do not reject the null hypothesis." Only one of two
hypotheses is true and the hypotheses cover all possible values of
the population parameter.
◉ What is the decision rule when using the p-value approach to
hypothesis testing? Answer: Reject Ho if the p-value < α.
