Question 1

The binomial test uses data to test whether a sample proportion matches the null expectation for the proportion.

Accepted Answer

A) True 
 B)False  False

Question 2

Consider a set of nine separate water samples from a region where the prevalence of bacterial contamination is 30%. Assuming the binomial distribution is appropriate, what is the probability that exactly three of the samples indicate contamination?

Accepted Answer

A)  0.267 
B)  0.333 
C)  0.350 
D)  0.400 
A)  0.267 
B)  0.333 
C)  0.350 
D)  0.400 A

Question 3

The term $\left(\begin{array}{c}
10 \
4
\end{array}\right)$ is stated verbally as "ten choose four."

Accepted Answer

A) True 
 B)False  True

Question 4

Consider a binomial distribution with a sample size of 10 and a success probability of 0.9. What is the probability that there are more than 8 successes?

Accepted Answer

A)  0.193 
B)  0.349 
C)  0.387 
D)  0.736 
A)  0.193 
B)  0.349 
C)  0.387 
D)  0.736

Question 5

When calculating binomial probabilities, we use the term "success" for the desired outcome of each individual trial.

Accepted Answer

A) True 
 B)False

Question 6

Imagine a surgery that is known to have a 10% chance of serious side effects. An internal hospital review shows that three out of eight of a particular doctor's patients have these side effects. If we conducted a binomial test of whether this doctor's patients are experiencing unusually low or high rates of side effects, what would our conclusion be?

Accepted Answer

A)  We fail to reject the null hypothesis and therefore conclude that the rate of side effects for this doctor differs from the usual 10%. 
B)  We fail to reject the null hypothesis and therefore conclude that the rate of side effects for this doctor does not seem to differ from the usual 10%. 
C)  We reject the null hypothesis and therefore conclude that the rate of side effects for this doctor differs from the usual 10%. 
D)  We reject the null hypothesis and therefore conclude that the rate of side effects for this doctor does not seem to differ from the usual 10%. 
A)  We fail to reject the null hypothesis and therefore conclude that the rate of side effects for this doctor differs from the usual 10%. 
B)  We fail to reject the null hypothesis and therefore conclude that the rate of side effects for this doctor does not seem to differ from the usual 10%. 
C)  We reject the null hypothesis and therefore conclude that the rate of side effects for this doctor differs from the usual 10%. 
D)  We reject the null hypothesis and therefore conclude that the rate of side effects for this doctor does not seem to differ from the usual 10%.

Question 7

Consider the claim that 60% of the members of a population of bacteria have a plasmid conferring antibiotic resistance. If we collected some random bacterial samples and the P-value of a binomial test was 0.15, what would our conclusion be?

Accepted Answer

A)  We fail to reject the null hypothesis and therefore conclude that the true proportion of bacteria with resistance plasmids differs from 60%. 
B)  We fail to reject the null hypothesis and therefore conclude that the true proportion of bacteria with resistance plasmids does not differ from 60%. 
C)  We reject the null hypothesis and therefore conclude that the true proportion of bacteria with resistance plasmids differs from 60%. 
D)  We reject the null hypothesis and therefore conclude that the true proportion of bacteria with resistance plasmids does not differ from 60%. 
A)  We fail to reject the null hypothesis and therefore conclude that the true proportion of bacteria with resistance plasmids differs from 60%. 
B)  We fail to reject the null hypothesis and therefore conclude that the true proportion of bacteria with resistance plasmids does not differ from 60%. 
C)  We reject the null hypothesis and therefore conclude that the true proportion of bacteria with resistance plasmids differs from 60%. 
D)  We reject the null hypothesis and therefore conclude that the true proportion of bacteria with resistance plasmids does not differ from 60%.

Question 8

What is the 95% confidence interval, using the Agresti-Coull method, for the proportion when there are 7 observed successes out of a total of 50 trials?

Accepted Answer

A)  0.014 < p < 0.213 
B)  0.044 < p < 0.236 
C)  0.067 < p < 0.266 
D)  0.104 < p < 0.282 
A)  0.014 < p < 0.213 
B)  0.044 < p < 0.236 
C)  0.067 < p < 0.266 
D)  0.104 < p < 0.282

Question 9

Consider a situation in which a group of ecologists are studying the frequency of symbiotic relationships between acacia trees and ant colonies in Bolivia. Previous studies in Colombia have shown the frequency of symbiotic relationships there to be 30%, and the ecologists are interested in whether the same frequency holds in Colombia. They locate 20 trees and determine that 11 of the trees appear to have a symbiotic relationship with an ant colony. Use a binomial test and the calculation of 95% confidence intervals to address this question: Is there sufficient evidence to determine whether the frequency of symbiotic acacia trees in Colombia differs from 30% or not?

Accepted Answer

To address the question of whether the f

Question 10

If a study with a total sample size of 14 measures 7 successes, in how many different sequences could these successes have occurred??

Accepted Answer

A)  3,003 
B)  3,432 
C)  3,867 
D)  4,124 
A)  3,003 
B)  3,432 
C)  3,867 
D)  4,124

Question 11

Consider the claim that 60% of the members of a population of bacteria have a plasmid conferring antibiotic resistance. If we collected some random bacterial samples and the P-value of a binomial test was 0.015, what would our conclusion be?

Accepted Answer

A)  We fail to reject the null hypothesis and therefore conclude that the true proportion of bacteria with resistance plasmids differs from 60%. 
B)  We fail to reject the null hypothesis and therefore conclude that the true proportion of bacteria with resistance plasmids does not differ from 60%. 
C)  We reject the null hypothesis and therefore conclude that the true proportion of bacteria with resistance plasmids differs from 60%. 
D)  We reject the null hypothesis and therefore conclude that the true proportion of bacteria with resistance plasmids does not differ from 60%. 
A)  We fail to reject the null hypothesis and therefore conclude that the true proportion of bacteria with resistance plasmids differs from 60%. 
B)  We fail to reject the null hypothesis and therefore conclude that the true proportion of bacteria with resistance plasmids does not differ from 60%. 
C)  We reject the null hypothesis and therefore conclude that the true proportion of bacteria with resistance plasmids differs from 60%. 
D)  We reject the null hypothesis and therefore conclude that the true proportion of bacteria with resistance plasmids does not differ from 60%.

Question 12

The value of 99! / 97! is which of the following?

Accepted Answer

A)  9,405 
B)  9,504 
C)  9,603 
D)  9,702 
A)  9,405 
B)  9,504 
C)  9,603 
D)  9,702

Question 13

Consider a situation in which a group of physiologists are studying the sizes of wings in seagulls. They are interested in whether the gulls show asymmetry or symmetry with respect to the wing sizes. They humanely trap (and subsequently release) 14 seagulls, and after measuring the wings they determine that 10 had larger right wings than left wings and 4 had larger left wings than right wings. Use a binomial test and the calculation of 95% confidence intervals to address this question: Is there sufficient evidence to determine whether the population of seagulls is symmetric with respect to their wing sizes or not?

Accepted Answer

To address the question of whether the p

Question 14

The value of $\left(\begin{array}{c}
11 \
7
\end{array}\right)$ is which of the following?

Accepted Answer

A)  77 
B)  330 
C)  7,920 
D)  37,290 
A)  77 
B)  330 
C)  7,920 
D)  37,290

Question 15

When calculating the standard error of a proportion, if the sample size is small or the population proportion is close to 0 or 1, then the Wald method is preferable to the Agresti-Coull method.

Accepted Answer

A) True 
 B)False

Question 16

Consider a bird has laid a clutch of six eggs that all hatch. Assuming the binomial distribution is appropriate, what is the probability that there is an equal number of male and female chicks that hatch?

Accepted Answer

A)  0.279 
B)  0.313 
C)  0.346 
D)  0.500 
A)  0.279 
B)  0.313 
C)  0.346 
D)  0.500

Question 17

Demonstrate with a hypothetical numerical example how the Agresti-Coull method generates a narrower confidence interval than the Wald method.

Accepted Answer

Sure, I can provide a hypothetical numer

Question 18

What is the 95% confidence interval, using the Wald method, for the proportion when there are 7 observed successes out of a total of 50 trials?

Accepted Answer

A)  0.014 < p < 0.213 
B)  0.044 < p < 0.236 
C)  0.074 < p < 0.259 
D)  0.104 < p < 0.282 
A)  0.014 < p < 0.213 
B)  0.044 < p < 0.236 
C)  0.074 < p < 0.259 
D)  0.104 < p < 0.282

Question 19

If a binomial test returns a P-value greater than 0.05, we typically interpret this as meaning there is a match between the data and our expectations arising from using the binomial distribution to model the population.

Accepted Answer

A) True 
 B)False

Question 20

Draw a bar chart showing the sampling distribution for the proportion of successes for sample size 3 where the population proportion of successes is 0.6. Clearly label each axis and be precise.

Accepted Answer

To create a bar chart showing the sampli

The binomial test uses data to test whether a sample proportion matches the null expectation for the proportion.

Consider a set of nine separate water samples from a region where the prevalence of bacterial contamination is 30%. Assuming the binomial distribution is appropriate, what is the probability that exactly three of the samples indicate contamination?

The term $\left(\begin{array}{c}10 \\4\end{array}\right)$ is stated verbally as "ten choose four."

Consider a binomial distribution with a sample size of 10 and a success probability of 0.9. What is the probability that there are more than 8 successes?

When calculating binomial probabilities, we use the term "success" for the desired outcome of each individual trial.

Consider the claim that 60% of the members of a population of bacteria have a plasmid conferring antibiotic resistance. If we collected some random bacterial samples and the P-value of a binomial test was 0.15, what would our conclusion be?

What is the 95% confidence interval, using the Agresti-Coull method, for the proportion when there are 7 observed successes out of a total of 50 trials?

If a study with a total sample size of 14 measures 7 successes, in how many different sequences could these successes have occurred??

Consider the claim that 60% of the members of a population of bacteria have a plasmid conferring antibiotic resistance. If we collected some random bacterial samples and the P-value of a binomial test was 0.015, what would our conclusion be?

The value of 99! / 97! is which of the following?

The value of $\left(\begin{array}{c}11 \\7\end{array}\right)$ is which of the following?

When calculating the standard error of a proportion, if the sample size is small or the population proportion is close to 0 or 1, then the Wald method is preferable to the Agresti-Coull method.

Consider a bird has laid a clutch of six eggs that all hatch. Assuming the binomial distribution is appropriate, what is the probability that there is an equal number of male and female chicks that hatch?

Demonstrate with a hypothetical numerical example how the Agresti-Coull method generates a narrower confidence interval than the Wald method.

What is the 95% confidence interval, using the Wald method, for the proportion when there are 7 observed successes out of a total of 50 trials?

If a binomial test returns a P-value greater than 0.05, we typically interpret this as meaning there is a match between the data and our expectations arising from using the binomial distribution to model the population.

Draw a bar chart showing the sampling distribution for the proportion of successes for sample size 3 where the population proportion of successes is 0.6. Clearly label each axis and be precise.

Statistics and Samples

Displaying Data

Describing Data

Estimating With Uncertainty

Probability

Hypothesis Testing

Fitting Probability Models to Frequency Data

Contingency Analysis: Associations Between

The Normal Distribution

Inference for a Normal Population

Comparing Two Means

Handling Violations of Assumptions

Designing Experiments

Comparing Means of More Than Two Groups

Correlation Between Numerical Variables

Regression

Multiple Explanatory Variables

Computer-Intensive Methods

Likelihood

Meta-Analysis: Combining Information From

Filters

Exam 7: Analyzing Proportions

The binomial test uses data to test whether a sample proportion matches the null expectation for the proportion.

Consider a set of nine separate water samples from a region where the prevalence of bacterial contamination is 30%. Assuming the binomial distribution is appropriate, what is the probability that exactly three of the samples indicate contamination?

The term (104)\left(\begin{array}{c}10 \\4\end{array}\right)(104​) is stated verbally as "ten choose four."

Consider a binomial distribution with a sample size of 10 and a success probability of 0.9. What is the probability that there are more than 8 successes?

When calculating binomial probabilities, we use the term "success" for the desired outcome of each individual trial.

Consider the claim that 60% of the members of a population of bacteria have a plasmid conferring antibiotic resistance. If we collected some random bacterial samples and the P-value of a binomial test was 0.15, what would our conclusion be?

What is the 95% confidence interval, using the Agresti-Coull method, for the proportion when there are 7 observed successes out of a total of 50 trials?

If a study with a total sample size of 14 measures 7 successes, in how many different sequences could these successes have occurred??

Consider the claim that 60% of the members of a population of bacteria have a plasmid conferring antibiotic resistance. If we collected some random bacterial samples and the P-value of a binomial test was 0.015, what would our conclusion be?

The value of 99! / 97! is which of the following?

The value of (117)\left(\begin{array}{c}11 \\7\end{array}\right)(117​) is which of the following?

When calculating the standard error of a proportion, if the sample size is small or the population proportion is close to 0 or 1, then the Wald method is preferable to the Agresti-Coull method.

Consider a bird has laid a clutch of six eggs that all hatch. Assuming the binomial distribution is appropriate, what is the probability that there is an equal number of male and female chicks that hatch?

Demonstrate with a hypothetical numerical example how the Agresti-Coull method generates a narrower confidence interval than the Wald method.

What is the 95% confidence interval, using the Wald method, for the proportion when there are 7 observed successes out of a total of 50 trials?

If a binomial test returns a P-value greater than 0.05, we typically interpret this as meaning there is a match between the data and our expectations arising from using the binomial distribution to model the population.

Draw a bar chart showing the sampling distribution for the proportion of successes for sample size 3 where the population proportion of successes is 0.6. Clearly label each axis and be precise.

Statistics and Samples

Displaying Data

Describing Data

Estimating With Uncertainty

Probability

Hypothesis Testing

Fitting Probability Models to Frequency Data

Contingency Analysis: Associations Between

The Normal Distribution

Inference for a Normal Population

Comparing Two Means

Handling Violations of Assumptions

Designing Experiments

Comparing Means of More Than Two Groups

Correlation Between Numerical Variables

Regression

Multiple Explanatory Variables

Computer-Intensive Methods

Likelihood

Meta-Analysis: Combining Information From

Filters

The term $\left(\begin{array}{c}10 \\4\end{array}\right)$ is stated verbally as "ten choose four."

The value of $\left(\begin{array}{c}11 \\7\end{array}\right)$ is which of the following?