Week 4 - Confidence Intervals

Question 1

Most common CIs?

Answer 1

90%, 95% or 99%

(0% to 100% are possible, though not usually desirable)

Question 2

Hypothesis testing involves generating an ____________ about the ___________ ____________.

Answer 2

hypothesis, population parameter

Question 3

Confidence Interval (CI) estimate…

Answer 3

Range or interval of values for parameters with a level of confidence attached (95% confidence that the interval contains the parameter)

Question 4

Why are confidence ‘intervals’ also called ‘confidence interval estimates’?

Answer 4

Because the method used to calculate confidence intervals is an estimation.

Question 5

Why Confidence Interval Estimate vs. Point Estimate?

Answer 5

Generally, point estimates are not accurate enough to provide information about the parameter, or the variability within the parameter.

Question 6

Estimation uses sample data to generate ________ in the population.

Answer 6

Parameters

Question 7

Do the properties of CLT hold if the population is normally distributed and the population is > 30?

Answer 7

Yes

Question 8

95% confidence interval means that

Answer 8

We are 95 % confident that interval contains mew

Question 9

When Student’s t Distribution?

Answer 9

1. Distribution not normal
2. n < 30

Question 10

What type of sample is used in confidence interval calculations?

Answer 10

Random sample is preferred.

Question 11

Measurements of sample population are called _________.

Answer 11

Parameters.

Question 12

What is Statistical Inference?

Answer 12

Process of reaching a conclusion about a population based on information from a sample of that population

Question 13

What is mu₁ - mu₂?

Answer 13

Difference in means

Question 14

In CI >= 30 formula, what are:

X bar,

Z,

s, and

n?

Answer 14

X bar = Point Estimate

Z = value from Z table

s = standard deviation

n = sample size

Question 15

What is Sp?

Answer 15

Pooled Estimate of Common Standard Deviation

Question 16

What is mu_d?

Answer 16

Mean difference

Question 17

How do you calculate confidence interval?

Answer 17

CI = point estimate +- margin of error

Point Estimate = X bar

Margin of Error = (Z*(s/(square root of ‘n’)))

therefore,

CI = X bar +- (Z*(s/(square root of ‘n’)))

*Z or t value, based on sample size*

Question 18

When do you use the CI estimation for mu_d?

Answer 18

1. When you have a continuous outcome, and
2. When you have two matched/paired samples,
3. Unit of analysis is a pair

Question 19

When do you use the CI estimation for mu?

Answer 19

1. When you have a continuous outcome, and
2. When you have a single sample, and
3. When you want to estimate for the population mean for that sample.

Question 20

Do the properties of CLT hold true if sample is < 30 and normally distributed?

Answer 20

Yes.

Question 21

What is formula for CI for mu_d?

Answer 21

Xbar_d = Σ(x₁ - x₂)/n

Question 22

In confidence interval estimates, _____________ gives the range of values above and below the ___________.

Answer 22

margin of error

point estimate

Question 23

Can you use t distribution for large n?

Answer 23

Yes, because when n is large, t is approximately equal to standard normal distribution (Z).

Question 24

The words ______ and ______ clues that we’re calculating Mean Difference.

Answer 24

before, after

pre, post

Question 25

To get a smaller interval, do what?

Answer 25

Either lower level of confidence or increase n.

Question 26

Measurements of sample data are called \_\_\_\_\_\_\_\_\_\_\_\_.

Answer 26

Statistics

Question 27

Types of Stastical Inference

Answer 27

1. Estimation 2. Hypothesis Testing

Question 28

Confidence Interval (formula)

Answer 28

CI = Point Estimate ± Margin of Error

Question 29

Disadvantages of using t-distribution to calculate confidence intervals:

Answer 29

1. Wider intervals 2. Must be able to assume that the underlying distribution is normal.

Question 30

Why Student's t Distribution?

Answer 30

1. n \< 30 2. Cannot use z distribution b/c CLT does not hold 3. Sample point estimates may not be reliable estimate of true population values

Question 32

Is the point estimate representative of the entire population?

Answer 32

No. It is based on one sample and does not consider the variability within the parameter.

Question 33

Explain mean difference.

Answer 33

Mean difference computes the mean (average) of differences between pre and post values. Measurements are dependent. Mean difference = Σ(X_a - X_b)/n Ex. BMI study...pre BMI (X_1a), post BMI (X_1b), sum of differences divided by n

Question 34

Mu, which represents the mean of the population is a \_\_\_\_\_\_\_\_\_\_. Parameter or Stastic

Answer 34

Parameter

Question 35

Estimation determines

Answer 35

likely values for an unknown population parameter.

Question 36

What is best single estimator for parameter (e.g., mean)?

Answer 36

Point estimate

Question 37

In CI \< 30 formula, what are: X bar, t, s, n?

Answer 37

X bar = Point Estimate t = value from t table s = standard deviation n = sample size

Question 38

True or False: There will always be some degree of uncertainty when you caculate point estimates based on your sample.

Answer 38

True

Question 39

Sample statistics are analyzed to...

Answer 39

support or reject the hypothesis about the parameter.

Question 40

Which is better? Confidence Interval or Point Estimate. Why?

Answer 40

Confidence Interval Estimates Generally, point estimates are not accurate enough to provide information about the parameter, or the variability within the parameter.

Question 41

Do the properties of CLT hold if the population is not normally distributed and \< 30?

Answer 41

No.

Question 42

What can be said about the sample drawn from the population in both estimation _and_ hypothesis testing?

Answer 42

The sample is random

Question 43

When estimating _difference in means_, what is formula for Point Estimate?

Answer 43

mu₁ - mu₂

Question 44

Explain difference of means.

Answer 44

Mean of all pre measurements - Mean of all post measurements Measurements are independent. Ex. Pre BMI (X_1a), Post BMI (X_1b) (Xbar_a - Xbar_b)

Question 45

Key Points (3) of Student's t Distribution?

Answer 45

1. It is a *set* of distributions, not a single distribution. Collectively, these sets assume the shape of a bell shaped curve. 2. Uses the parameter, degrees of freedom (df) df = n-1 3. If n is sufficiently large, student's distribution (t) is approximately equal to standard distribution (z)

Question 46

X bar, represents the sample mean of a \_\_\_\_\_\_\_\_\_\_. Parameter or Stastic

Answer 46

Statistic

Question 47

Do the properties of CLT hold true if the population \< 30 and normally distributed?

Answer 47

Yes.