Question 1

We are about to test a hypothesis using data from a well-designed study. Which is true?
I. A large P-value would be strong evidence against the null hypothesis.
II. We can set a higher standard of proof by choosing α = 10% instead of 5%.
III. If we reduce the risk of committing a Type I error, then the risk of a Type II error will also
Decrease.
A) III only
B) II only
C) none of these
D) I only
E) I and II only

Accepted Answer

A large P-value indicates weak evidence against the null hypothesis, not strong evidence. Setting α = 10% instead of 5% lowers the standard of proof, not raises it. Reducing the risk of a Type I error (by lowering α) generally increases the risk of a Type II error, not decreases it.

Question 2

We test the hypothesis that $p = 35 \%$ versus $p < 35 \%$. We don't know it but actually $p = 26 \%$. With which sample size and significance level will our test have the greatest power?
A) $\alpha = 0.01 , n = 400$
B) $\alpha = 0.03 , n = 250$
C) $\alpha = 0.01 , n = 250$
D) $\alpha = 0.03 , n = 400$
E) The power will be the same as long as the true proportion $p$ remains $26 \%$

Accepted Answer

The power of a test increases with a larger sample size and a higher significance level. Option D has both a larger sample size and a higher significance level compared to the other options.

Question 3

Depression A recent psychiatric study from the University of Southampton observed a
higher incidence of depression among women whose birth weight was less than 6.6
pounds than in women whose birth weight was over 6.6 pounds. Based on a P-value of
0.0248 the researchers concluded there was evidence that low birth weights may be a risk
factor for susceptibility to depression. Explain in context what the reported P-value means.

Accepted Answer

The answer of Depression A recent psychiatric study from the...

Question 4

An online catalog company wants on-time delivery for at least 90% of the orders they ship. They Have been shipping orders via UPS and FedEx but will switch to a more expensive service (ShipFast) if there is evidence that this service can exceed the 90% on-time goal. As a test the Company sends a random sample of orders via ShipFast, and then makes follow-up phone calls to See if these orders arrived on time. Which hypotheses should they test? A) $\mathrm { H } _ { 0 } : p = 0.90$ $\mathrm { H } _ { \mathrm { A } } : p < 0.90$ B) $\mathrm { H } _ { 0 } : p < 0.90$ $\mathrm { H } _ { \mathrm { A } } : p = 0.90$ C) $\mathrm { H } _ { 0 } : p = 0.90$ $\mathrm { H } _ { \mathrm { A } } : p > 0.90$ D) $\mathrm { H } _ { 0 } : p > 0.90$ $\mathrm { H } _ { \mathrm { A } } : p = 0.90$ E) $\mathrm { H } _ { 0 } : p = 0.90$ $\mathrm { H } _ { \mathrm { A } } : p \neq 0.90$

Accepted Answer

The company wants to see if ShipFast can exceed the 90% on-time delivery goal, so the null hypothesis should be that the on-time delivery rate is 90% ($H_0: p = 0.90$), and the alternative hypothesis should be that the on-time delivery rate is greater than 90% ($H_A: p > 0.90$).

Question 5

We are about to test a hypothesis using data from a well-designed study. Which is true?
I. A small P-value would be strong evidence against the null hypothesis.
II. We can set a higher standard of proof by choosing α = 10% instead of 5%.
III. If we reduce the alpha level, we reduce the power of the test.
A) none of these
B) I and III only
C) I only
D) III only
E) II only

Accepted Answer

A small P-value indicates strong evidence against the null hypothesis (I is true). Reducing the alpha level (e.g., from 5% to 1%) decreases the probability of a Type I error but also reduces the power of the test (III is true).

Question 6

Truckers On many highways state police officers conduct inspections of driving logbooks from
large trucks to see if the trucker has driven too many hours in a day. At one truck inspection
station they issued citations to 49 of 348 truckers that they reviewed.
a. Based on the results of this inspection station, construct and interpret a 95% confidence interval
for the proportion of truck drivers that have driven too many hours in a day.
b. Explain the meaning of "95% confidence" in part A.

Accepted Answer

The answer of Truckers On many highways state police officers...

Question 7

A pharmaceutical company investigating whether drug stores are less likely than food markets to
Remove over-the-counter drugs from the shelves when the drugs are past the expiration date
Found a P-value of 2.8%. This means that:
A) none of these
B) There is a 2.8% chance the drug stores remove more expired over-the-counter drugs.
C) 2.8% more drug stores remove over-the-counter drugs from the shelves when the drugs are past the expiration date.
D) There is a 97.2% chance the drug stores remove more expired over-the-counter drugs.
E) 97.2% more drug stores remove over-the-counter drugs from the shelves when the drugs are past the expiration date than drug stores.

Accepted Answer

A P-value of 2.8% indicates that there is a 2.8% probability of observing the data, or something more extreme, assuming the null hypothesis is true. It does not directly provide probabilities about the actions of drug stores or percentages of stores removing drugs.

Question 8

To plan the course offerings for the next year a university department dean needs to estimate what
Impact the "No Child Left Behind" legislation might have on the teacher credentialing program.
Historically, 40% of this university's pre-service teachers have qualified for paid internship
Positions each year. The Dean of Education looks at a random sample of internship applications to
See what proportion indicate the applicant has achieved the content-mastery that is required for
The internship. Based on these data he creates a 90% confidence interval of (33%, 41%). Could this
Confidence interval be
Used to test the hypothesis H0: p = 0.40 versus HA: p < 0.40 at the α = 0.05 level of significance?
A) Yes, since 40% is in the confidence interval he fails to reject the null hypothesis, concluding that there is not strong enough evidence of any change in the percent of qualified applicants.
B) Yes, since 40% is not the center of the confidence interval he rejects the null hypothesis, concluding that the percentage of qualified applicants will decrease.
C) No, because the dean only reviewed a sample of the applicants instead of all of them.
D) Yes, since 40% is in the confidence interval he accepts the null hypothesis, concluding that the percentage of applicants qualified for paid internship positions will stay the same.
E) No, because he should have used a 95% confidence interval.

Accepted Answer

The 90% confidence interval includes 40%, so there is not enough evidence to reject the null hypothesis at the 0.05 significance level.

Question 9

Suppose that a device advertised to increase a car's gas mileage really does not work. We test it on a small fleet of cars (with $\mathrm { H } _ { 0 }$ : not effective), and our data results in a $P$-value of $0.004$. What probably happens as a result of our experiment?
A) We fail to reject $\mathrm { H } _ { 0 }$, committing Type II error.
B) We correctly fail to reject $\mathrm { H } _ { 0 }$.
C) We reject $\mathrm { H } _ { 0 }$, making a Type I error.
D) We reject $\mathrm { H } _ { 0 }$, making a Type II error.
E) $\mathrm { We }$ correctly reject $\mathrm { H } _ { 0 }$.

Accepted Answer

A low P-value (0.004) suggests strong evidence against $\mathrm { H } _ { 0 }$, leading us to reject it, but since $\mathrm { H } _ { 0 }$ is true, this results in a Type I error.

Question 10

A truck company wants on-time delivery for 98% of the parts they order from a metal Manufacturing plant. They have been ordering from Hudson Manufacturing but will switch to a New, cheaper manufacturer (Steel-R-Us) unless there is evidence that this new manufacturer Cannot meet the 98% on-time goal. As a test the truck company purchases a random sample of Metal parts from Steel-R-Us, and then determines if these parts were delivered on-time. Which Hypothesis should they test? A) $\mathrm { H } _ { 0 } : p = 0.98$ $\mathrm { H } _ { \mathrm { A } } : p < 0.98$ B) $\mathrm { H } _ { 0 } : p < 0.98$ $\mathrm { H } _ { \mathrm { A } } : p > 0.98$ C) $\mathrm { H } _ { 0 } : p = 0.98$ $\mathrm { H } _ { \mathrm { A } } : p \neq 0.98$ D) $\mathrm { H } _ { 0 } : p = 0.98$ $\mathrm { H } _ { \mathrm { A } } : p > 0.98$ E) $\mathrm { H } _ { 0 } : p > 0.98$ $\mathrm { H } _ { \mathrm { A } } : p = 0.98$

Accepted Answer

The null hypothesis ($H_0$) should state that the on-time delivery rate is 98% ($p = 0.98$), and the alternative hypothesis ($H_A$) should test if the rate is less than 98% ($p < 0.98$), indicating that the new manufacturer cannot meet the goal.

Question 11

A certain population is strongly skewed to the left. We want to estimate its mean, so we collect a
Sample. Which should be true if we use a large sample rather than a small one?
I. The distribution of our sample data will be more clearly skewed to the left.
II. The sampling model of the sample means will be more skewed to the left.
III. The variability of the sample means will greater.
A) I only
B) I and III only
C) II only
D) II and III only
E) III only

Accepted Answer

The answer of A certain population is strongly skewed to...

Question 12

Graduation tests Many states mandate tests that have to be passed in order for students to
graduate with a high school diploma. A local school superintendent believes that
after-school tutoring will improve the scores of students in his district on the state's
graduation test. A tutor agrees to work with 15 students for a month before the
superintendent will approach the school board about implementing an after-school
tutoring program. The after-school tutoring program will be implemented if student
scores increase by more than 20 points. The superintendent will test a hypothesis using α =
0.02 .
a. Write appropriate hypotheses (in words and in symbols).
b. In this context, which do you consider to be more serious - a Type I or a Type II error?
Explain.
c. After this trial produced inconclusive results, the superintendent decided to test the
after-school tutoring program again with another group of students. Describe two changes
he could make in the trial to increase the power of the test, and explain the disadvantages
of each.

Accepted Answer

The answer of Graduation tests Many states mandate tests that...

Question 13

A researcher investigating whether joggers are less likely to get colds than people who do not jog
Found a P-value of 3%. This means that:
A) none of these
B) 3% of joggers get colds.
C) There's a 3% chance that joggers don't get fewer colds.
D) Joggers get 3% fewer colds than non-joggers.
E) There's a 3% chance that joggers get fewer colds.

Accepted Answer

The P-value of 3% indicates that there is a 3% probability of observing the data, or something more extreme, assuming the null hypothesis is true. It does not directly relate to the percentage of joggers getting colds or the chance that joggers get fewer colds.

Question 14

Suppose that a conveyor used to sort packages by size does not work properly. We test the conveyor on several packages (with $H _ { 0 }$ : incorrect sort) and our data results in a $P$-value of $0.016$. What probably happens as a result of our testing?
A) Correctly reject $\mathrm { H } _ { 0 }$.
B) Reject $\mathrm { H } _ { 0 }$, making a Type II error.
C) Fail to reject $\mathrm { H } _ { 0 }$, committing a Type II error.
D) Correctly fail to reject $\mathrm { H } _ { 0 }$.
E) Reject $\mathrm { H } _ { 0 }$, making a Type I error.

Accepted Answer

The answer of Suppose that a conveyor used to sort...

Question 15

We have calculated a confidence interval based on a sample of n = 180. Now we want to get a better
Estimate with a margin of error only one third as large. We need a new sample with n at least…
A) 60
B) 540
C) 312
D) 1620
E) 20

Accepted Answer

To reduce the margin of error to one third, the sample size must be increased by a factor of nine (since the margin of error is inversely proportional to the square root of the sample size). Therefore, the new sample size should be 180 * 9 = 1620.

Question 16

Which is true about a 95% confidence interval based on a given sample?
I. The interval contains 95% of the population.
II. Results from 95% of all samples will lie in the interval.
III. The interval is narrower than a 98% confidence interval would be.
A) none of these
B) III only
C) II only
D) I only
E) II and III only

Accepted Answer

A 95% confidence interval is narrower than a 98% confidence interval because a higher confidence level requires a wider interval to ensure that the parameter is captured.

Question 17

Dolphin births A state has two aquariums that have dolphins, with more births recorded
at the larger aquarium than at the smaller one. Records indicate that in general babies are
equally likely to be male or female, but the gender ratio varies from season to season.
Which aquarium is more likely to report a season when over two-thirds of the dolphins
born were males? Explain.

Accepted Answer

The answer of Dolphin births A state has two aquariums...

Question 18

Which is true about a 99% confidence interval based on a given sample?
I. The interval contains 99% of the population.
II. Results from 99% of all samples will lie in this interval.
III. The interval is wider than a 95% confidence interval would be.
A) II and III only
B) III only
C) II only
D) I only
E) none of these

Accepted Answer

A 99% confidence interval is wider than a 95% confidence interval because it reflects greater uncertainty and aims to capture the true population parameter with higher confidence.

Question 19

Approval rating A newspaper article reported that a poll based on a sample of 1150
residents of a state showed that the state's Governor's job approval rating stood at 58%.
They claimed a margin of error of ±3%. What level of confidence were the pollsters using?

Accepted Answer

The answer of Approval rating A newspaper article reported that...

Question 20

Pumpkin pie A can of pumpkin pie mix contains a mean of 30 ounces and a standard
deviation of 2 ounces. The contents of the cans are normally distributed. What is the
probability that four randomly selected cans of pumpkin pie mix contain a total of more
than 126 ounces?

Accepted Answer

The answer of Pumpkin pie A can of pumpkin pie...

Quiz 8: Regression, Associations, and Predictive Modeling

We test the hypothesis that $p = 35 \%$ versus $p < 35 \%$ . We don't know it but actually $p = 26 \%$ . With which sample size and significance level will our test have the greatest power?

A pharmaceutical company investigating whether drug stores are less likely than food markets to Remove over-the-counter drugs from the shelves when the drugs are past the expiration date Found a P-value of 2.8%. This means that:

Suppose that a device advertised to increase a car's gas mileage really does not work. We test it on a small fleet of cars (with $\mathrm { H } _ { 0 }$ : not effective) , and our data results in a $P$ -value of $0.004$ . What probably happens as a result of our experiment?

A researcher investigating whether joggers are less likely to get colds than people who do not jog Found a P-value of 3%. This means that:

Suppose that a conveyor used to sort packages by size does not work properly. We test the conveyor on several packages (with $H _ { 0 }$ : incorrect sort) and our data results in a $P$ -value of $0.016$ . What probably happens as a result of our testing?

We have calculated a confidence interval based on a sample of n = 180. Now we want to get a better Estimate with a margin of error only one third as large. We need a new sample with n at least…

Which is true about a 95% confidence interval based on a given sample? I. The interval contains 95% of the population. II. Results from 95% of all samples will lie in the interval. III. The interval is narrower than a 98% confidence interval would be.

Which is true about a 99% confidence interval based on a given sample? I. The interval contains 99% of the population. II. Results from 99% of all samples will lie in this interval. III. The interval is wider than a 95% confidence interval would be.

Approval rating A newspaper article reported that a poll based on a sample of 1150 residents of a state showed that the state's Governor's job approval rating stood at 58%. They claimed a margin of error of ±3%. What level of confidence were the pollsters using?

Pumpkin pie A can of pumpkin pie mix contains a mean of 30 ounces and a standard deviation of 2 ounces. The contents of the cans are normally distributed. What is the probability that four randomly selected cans of pumpkin pie mix contain a total of more than 126 ounces?