Statistics Chapter 7

Question 1

Target Parameter

Answer 1

the unknown population parameter (e.g. mean or proportion) that we are interested in estimating

Question 2

What key words are associated with the target parameters:
-μ
-p
-σ^2

Answer 2

-mean; average
-Quantitative

-proportion; percentage; fraction; rate
-Qualitative

-variance; variability; spread
-Quantitative

Question 3

Point Estimator of population

Answer 3

a rule or formula that tells us how to use the sample data to calculate a single number that can be used as an estimate of the target parameter

Question 4

Interval Estimator (confidence interval)

Answer 4

a formula that tells us how to use the sample data to calculate an interval and estimates the target parameter

Question 5

Confidence Coefficient

Answer 5

the probability that an interval estimator encolses the population parameter- that is, the relative frequency with which the interval estimator encloses the population parameter when the estimator is used repeatedly a very large number of times

Question 6

Confidence Level

Answer 6

the confidence coefficient expressed as a percentage

Question 7

zα

Answer 7

the value of the standard normal random variable z such that the area α will lie o its right.

P (z > zα) = α

Question 8

How big should a sample size be?

Answer 8

greater than or equal to 30

Question 9

Central Limit Theorem

Answer 9

Consider a random sample of n observations selected from a population (any population) with mean μ and standard deviation σ. Then, when n is sufficiently large, the sampling distribution of x̄ will be approximately a normal distribution with mean μx̄ = μ and standard deviation
σx̄ = σ / sqrt(n). The larger the sample size, the better will be the normal approximation to the sampling distribution of x̄

because of the CLT, the sum of random sample of n observations, the sum of x, will possess a sampling distribution that is approximately normal for large samples. This distribution will have a mean equal to (n) x (μ) and a variance equal to (n) x (σ)^2

Question 10

Confidence Interval for Population Mean

Answer 10

the level of confidence in the interval with a statement such as “We can be ___% confident that

Question 11

What conditions are required for a valid small-sample confidence interval for

Question 12

What conditions are required for a valid small-sample confidence interval for μ?

Answer 12

1. A random sample is selected from the target population.
2. The population has a relative frequency distribution that is approximately normal.

Question 13

p̂

Answer 13

sample proportion

sample mean fraction of success

Question 14

What’s the mean of the sampling distribution of p̂?

Answer 14

p

This only applies if p̂ is an unbiased estimator of p

Question 15

Formula for the standard deviation of the sampling distribution of p̂?

Answer 15

σp = sqrt( (p x q)/n )

Question 15

Formula for the standard deviation of the sampling distribution of p̂?

Answer 15

σp = sqrt( (p x q)/n )

Question 16

For large samples, what type of graph is the sampling distribution of p̂?

Answer 16

approximately normal

Question 17

When is a sample size considered large?

Answer 17

when both: (n x p̂) are greater than or equal to 15; (n x q̂) are greater than or equal to 15

Question 18

What conditions are required for a valid large-sample confidence interval for p?

Answer 18

1. A random sample is selected from the target population.
2. The sample size n is large. (This condition will be satisfied if both (n x p̂) are greater than or equal to 15; (n x q̂) are greater than or equal to 15. Note that (n x p̂) and (n x q̂) are simply the number of successes and number
   of failures, respectively, in the sample

Question 19

How do you find the Confidence Interval for a population mean (with a known σ or n is greater than or equal to 30)?

Question 20

How to create a confidence interval for a population mean (when n is less than 30)?