Exam #1: Biostatistics III

Question 1

What is a sampling distribution?

Answer 1

The probability distribution of the statistic

Question 2

What is an unbiased estimate of the parameter?

Answer 2

When the mean of the sampling distribution of a statistic can be shown to be equal to the parameter being estimated

Question 3

What is a biased estimate of the parameter?

Answer 3

When the mean of the sampling distribution is NOT equal to the parameter

Question 4

What is the formula for standard deviation of the sampling distribution?

Answer 4

Standard deviation of sampled population/ square root of the sample size

Question 5

What is another name of the standard deviation of the sampling distribution?

Answer 5

Standard error of the mean

Question 6

What is z?

Answer 6

Standard normal statistic

Question 7

Write the formula for z.

Answer 7

Sample mean - population mean/ standard error of the mean

Question 8

What is the central limit theorem?

Answer 8

With a sufficiently large random sample, the distribution will be normal

Question 9

In the central limit theorem, what happens as the sample size gets larger?

Answer 9

Sample distribution becomes almost normal

Question 10

What is the sample statistic in a confidence interval?

Answer 10

Point estimate around which the upper and lower confidence limits are set

Question 11

What is a confidence interval for a population mean?

Answer 11

A range of plausible values for the population mean

Question 12

Write the formula for calculating the confidence interval.

Answer 12

N/A

Question 13

What is the margin of error for 95% confidence?

Answer 13

1.96

Question 14

What is the margin of error for 99% confidence?

Answer 14

2.58

Question 15

What happens to the area under the curve with a higher confidence interval?

Answer 15

Gets larger

Question 16

What does a 95% confidence interval mean?

Answer 16

• 95% of the confidence intervals will contain u

- 5% will NOT

Question 17

What conditions need to be satisfied for a valid confidence interval?

Answer 17

• Random sample

- n must be large

Question 18

What is the difference between the standard normal statistic (z) and t-statistic?

Answer 18

S replaces the population standard deviation

Question 19

What are degrees of freedom?

Answer 19

• Variability in the sampling distribution of t depends on the sample size, n
• A way of expressing this is the “degrees of freedom”, calculated as (n-1)

Question 20

What can the sampling error be used to determine?

Answer 20

Necessary sample size to have a specific margin of error/ confidence

Question 21

What is a statistical hypothesis?

Answer 21

A statement about the numerical value of a population parameter

Question 22

What is the null hypothesis?

Answer 22

Hypothesis that will be accepted unless the data provides evidence it is false

Question 23

What is the alternative hypothesis?

Answer 23

Hypothesis that will be accepted only if the data provide evidence it is true

Question 24

Write the three ways of stating the alternative hypothesis.

Answer 24

N/A

Question 25

When do we use hypothesis testing?

Answer 25

1) Observational studies

2) Clinical trials

Question 26

What is a test statistic?

Answer 26

• A sample statistic

- Used to decide between null and alternative hypothesis

Question 27

What is a Type I Error?

Answer 27

• Null hypothesis rejected when it is in fact correct

- Denoted as alpha

Question 28

What is a Type II Error?

Answer 28

• Accepting the null hypothesis when the alternative hypothesis is correct
• Denoted as Beta

Question 29

What is the rejection region?

Answer 29

Set of possible values of the test statistic for which the researcher will reject null in favor of alternative

Question 30

What happens if a test statistic falls in the rejection region?

Answer 30

Reject the null hypothesis and accept the alternative

Question 31

What is a p-value in a hypothesis test?

Answer 31

Observed significance level
- Probability of observing a value of test statistic that is at least as contradictory to the null hypothesis as the actual one computed from sample data