Topic 2 : Confidence Intervals

Question 1

What is a confidence interval? (2)

2 components in 1 sentence

Answer 1

A type of inferential statistic that specifies a range of values that we use to estimate an unknown parameter

Question 2

Point estimate+ex (2)

Answer 2

• A single statitic that is used as our best estimate of an unknown population parameter, based on sample
• E.g., mean number of Facebook friends among people under 35 is 220

Question 3

Interval estimate + ex (2)

Answer 3

• A range of values within which the population parameter is likely to fall
• ex: people under 35 have between 200 and 240 Facebook friends

Question 4

Most unbaised point estimate of the population mean μ is the

Answer 4

sample mean x̄

Question 5

Level of Confidence

Answer 5

Specifies the probability that our interval estimate will in fact contain the population parameter

Question 6

Confidence level +ex (2)

Answer 6

• Specifies the probability that the population parameter will indeed lie within that specfied range of values
• Ex: We are 95% confident that the true population mean number of facebook friends fall within a range of 200 to 240 friends

Question 7

The higher the level of confidence, the — the confidence interval

Answer 7

wider

Question 8

The higher the sample size, the —- the confidence interval

Answer 8

narrower

Question 9

Sampling error (2)

What it is+ unknown

Answer 9

• The gap between sample statistics and the population parameters
• The true amount of sampling error is usually unkown because the parameter is unknown

Question 10

The margin of error (E) is

Answer 10

an estimate of the maximum amount of difference that we think is possible between our statistic and its coresponding parameter

Question 11

Difference between sampling error and margin of error

Answer 11

• sampling error is the gap betweeen sample statistics and population parameters while the MOE is an estimate of the maximium amount of difference we think is possible between our statistic and its coressponding parameter

Question 12

critical value of Z for 90% confidence

Answer 12

1.645

Question 13

What is C?

Answer 13

The area under the standard normal curve between critical values

Question 14

The conditions for calculating a confidence interval for the mean:

Answer 14

• the distribution of the population is assumed to be normal
• Data is obtained by random sampling

Question 15

Calculating margin of error when the standard deviation is known (3):

Answer 15

• Use Z and the normal distribution to determine the critical value
• use σ to calculate the standard error
• Multiple tgt

Question 16

Calculating margin of error when the standard deviation is not known (3):

Answer 16

Question 17

Calculation confidence intervals for μ (σ known) (4)

Answer 17

1. Find the sample statistic (Sample mean)
2. Find the critical Zc that coressponds to the given level of confidence
3. Find the Margin of Error with [E= Zc (σ/√n)]
4. Find the left and right end points and form the CI (x̄+/- E)

Question 18

Explain the results of a 95% confidence interval

Answer 18

If a large number of samples is collected and a confidence interval is created for each sample, approximatelt 95% of these intervals will contain μ.

Question 19

What if we raise the level of confidence? What is the trade off?

Answer 19

Your interval will get wider

Question 20

What happens if you increase the sample size when calculating confidence interval? Given that standard deviation is the same? (2)

interval estimate+ Confidence interval

Answer 20

• The chances that your interval estimate does not contain the parameter will be reduced
• Confidence interval will be narrower

Question 21

How to find the confidence interval if σ is unknown?

Answer 21

• When n> 30, can estimate σ with s and it will be reasonably accurate to use the Z-table to find the critical values and calculate our margin of error and CI
• When n < 30 or if we want to be more percise, we can use a distribution that has more area under the curve in the tails so we are not underestimating our margin of error

Question 22

T- distribution (2)

What is it+ When is it used

Answer 22

• a family of curves each determined by a parameter called the degrees of freedom
• The t-distribution is used in statistics to estimate the significance of population parameters for small sample sizes or unknown variations

Question 23

T distribution and sample size relationship

Answer 23

The T-distribution changes, depending on the sample size. The bigger the sample size, the more it looks like a normal distribution

Question 24

As the degrees of freedom increases, the t-distribution

Answer 24

approaches the normal distribution

Question 25

After —-, the t-distribution is very close to the standard normal Z-distribution

Answer 25

DF= 29 (n=30)

Question 26

Tell me about the tails in the t-distribution and standard normal distribution

Answer 26

The tails in T-distributions are thicker to help us not underestimate our confidence interval

Question 27

Steps for confidence interval for the population mean μ when σ unknown and n<30. (4)

Answer 27

4. Find the margin of error using E= tc (S/√n)
5. Find the left and right end points and form the CI (x̄+/- E)

Question 28

Confidence intervals are a type of —-

Answer 28

inferential statistics

Question 29

We use confidence interval for the —-

Distribu+organiz levels

Answer 29

• mean for normally distributed interval or ratio level variables