Ch. 1 - Confidence Intervals

Question 1

Population

Answer 1

A theoretical group you want to draw conclusions about.

Question 2

Sample

Answer 2

A subgroup selected – often at random – from a population.

Question 3

Parameter

Answer 3

A numeric summary of a population.

Ex: Population mean, μ (mu)

Question 4

Statistic

Answer 4

A numeric summary of a sample.

Ex: Sample mean, x̄ (x bar)

Question 5

Sample statistics are used to ESTIMATE __________.

Answer 5

population parameters

Question 6

The sample mean, x̄, is a __________ of the population mean, μ.

Answer 6

point estimate

Question 7

Sampling Distribution

Answer 7

The distribution of all possible sample means given a particular sample size, n.

Suppose that we draw all possible samples of size n from a given population. Suppose further that we compute a statistic (e.g., a mean, proportion, standard deviation) for each sample. The probability distribution of this statistic is called a sampling distribution.

Question 8

The sampling distribution is __________ when the sample size is large, n ≥ 30.

Answer 8

normally distributed

Question 9

The mean of the sampling distribution, μ_x̄ , is _____ to the mean of the sampled population, μ.

Answer 9

equal

μ_x̄ = μ

Question 10

Standard Error (SE or σ_{<em>x̄ ​</em>})

Answer 10

The standard deviation of the sampling distribution.

Question 11

Confidence Level

Answer 11

A confidence level refers to the percentage of all possible samples that can be expected to include the true population parameter.

In a survey sampling, different samples can be randomly selected from the same population; and each sample can often produce a different confidence interval. Some confidence intervals include the true population parameter; others do not.

For example, suppose all possible samples were selected from the same population, and a confidence interval were computed for each sample. A 95% confidence level implies that 95% of the confidence intervals would include the true population parameter.

Question 12

Confidence Interval

Answer 12

A range of values that is likely to contain a population parameter with a certain level of confidence. It terminates in an upper bound and a lower bound.

Question 13

Alpha, α

Answer 13

Alpha refers to the likelihood that the true population parameter lies outside the confidence interval. Alpha is usually expressed as a proportion. Thus, if the confidence level is 95%, then alpha would equal 1 - 0.95 or 0.05.

Question 14

Z confidence intervals are used for a population mean when the __________, σ, is _____.

Answer 14

standard deviation of the population (A.K.A. the standard deviation of the “sampled distribution”);
known

Question 15

Define each portion of the equation.

Answer 15

Question 16

How does the z-confidence interval determine upper and lower bounds?

Answer 16

Question 17

T confidence intervals are used for a population mean when the __________, σ, is _____.

Answer 17

standard deviation of the population (A.K.A. the standard deviation of the “sampled distribution”);
unknown

Question 18

Define each portion of the T-interval equation.

Question 19

The curve of the t-distribution has a shape like that of the __________.

Answer 19

standard normal curve

Question 20

The t curve is symmetrical about _____.

Answer 20

zero

Question 21

The mean of any t-distribution is _____.

Answer 21

zero

Question 22

The spread or standard deviation of the t-distribution is determined by one parameter, the number of __________.

Answer 22

degrees of freedom (denoted by df )

Question 23

As the sample size n increases, the spread of the t-distribution _____.

Answer 23

decreases

Question 24

As the number of degrees of freedom approaches infinity, the curve of the t-distribution approaches the curve of the __________.

Answer 24

standard normal

Question 25

The Standard Error (SE) of the estimate x̄ is the __________.

Answer 25

point estimate of σ_x̄

Question 26

Define each portion of the equation.

Answer 26