Exam 7: Analyzing Proportions

Imagine a surgery that is known to have a 10% chance of serious side effects. An internal hospital review shows that four out of eight of a particular doctor's patients have these side effects. If we want to know whether this doctor's patients are experiencing usually low or high rates of side effects, what would the P-value of a binomial test of this hypothesis be?

If a study with a total sample size of 15 measures 6 successes, in how many different sequences could these successes have occurred??

Using the Agresti-Coull method, what is the 95% confidence interval for the proportion when there are 15 observed successes and 25 observed failures?

If we have a sample with 50 values and a sample proportion of 0.40, what would the standard error of the proportion be?

If the 95% confidence interval for the proportion does not include the value hypothesized in the binomial test, then the test will almost certainly return a P-value greater than 0.05.

Imagine that we are rolling a six-sided die and we do that seven times. What is the probability that we roll a "one" either six or seven times?

The value of 8! / 5! is which of the following?

Consider the claim that 60% of the members of a population of bacteria have a plasmid conferring antibiotic resistance. If we collected 11 bacterial samples and 3 proved to have the resistance plasmid, what would the P-value of a binomial test of this hypothesis be?

The value of 7! is which of the following?

Using the Wald method, what is the 95% confidence interval for the proportion when there are 15 observed successes and 25 observed failures?

If we have a sample with 25 values and a sample proportion of 0.36, what would the standard error of the proportion be?

The term $\left(\begin{array}{l}7 \\3\end{array}\right)$ is stated verbally as "three choose seven."

What is the relationship between the 95% confidence interval for a proportion and the P-value of a binomial test?

If a study reveals 10 successes and 12 failures, in how many different ways (i.e., sequences) could this have occurred??

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 want to know whether this doctor's patients are experiencing unusually low or high rates of side effects, what would the P-value of a binomial test of this hypothesis be?

What is the standard error of the proportion when the sample size is 81 values and the sample proportion is 0.35?

When the binomial test returns a P-value less than 0.05, that generally means that the data match the expectations arising from using the binomial distribution to model the population.

The standard error of a proportion is used to estimate how much variation there is in the sample data.

Consider a class of 10 students in a school district with a 20% prevalence of students with special needs. Assuming the binomial distribution is appropriate, what is the probability that exactly 2 of those students have special needs?

When we do a binomial test and obtain a P-value smaller than 0.05, then the 95% confidence interval for the proportion will almost certainly not include the proportion we hypothesized.