# Confidence Interval Estimation Flashcards

1
Q

Point estimate

A

A point estimate is the value of a single sample statistic.

2
Q

Confidence interval

A

A confidence interval provides a range of values constructed around the point estimate.

3
Q

Confidence interval estimation

A

An interval gives a range of values: Takes into consideration variation in sample statistics from sample to sample. Based on observations from 1 sample.
Gives information about closeness to unknown population parameters.
Stated in terms of level of confidence. Can never be 100% confident.

4
Q

Common confidence intervals

A
```Common confidence levels = 90%, 95% or 99%:
Also written (1 - ) = 0.90, 0.95 or 0.99```
5
Q

A relative frequency interpretation

A

In the long run, 90%, 95% or 99% of all the confidence intervals that can be constructed (in repeated samples) will contain the unknown true parameter.

6
Q

Specific intervals

A

A specific interval will either contain or will not contain the true parameter. No probability involved in a specific interval.

7
Q

Confidence Interval for μ (σ Known) assumptions

A

Assumptions:
Population standard deviation σ is known
Population is normally distributed
If population is not normal, use Central Limit Theorem.

8
Q

Will the true average always be in the middle of the confidence interval

A

Not necessarily. PHOTO 9, A good but not perfect measure

9
Q

Confidence interval for μ (σ Unknown)

A

If the population standard deviation σ is unknown, we can substitute the sample standard deviation, S.
This introduces extra uncertainty, since S is variable from sample to sample.

So we use the Student t distribution instead of the normal distribution:
The t value depends on degrees of freedom denoted by sample size minus 1 i.e. (d.f = n - 1).

d.f are number of observations that are free to vary after sample mean has been calculated.

10
Q

Degrees of freedom

A

: Number of observations that are free to

vary after sample mean has been calculated

11
Q

Confidence interval example interpretation PHOTO

A

We are 95% confident that the true percentage of left-handers in the population is between 0.1651 and 0.3349 i.e.:

`	16.51% and 33.49%  `

Although the interval from 0.1651 to 0.3349 may or may not contain the true proportion, 95% of intervals formed from repeated samples of size 100 in this manner will contain the true proportion.

12
Q

Sampling error

A

The required sample size can be found to reach a desired margin of error (e) with a specified level of confidence (1 - alpha).

The margin of error is also called a sampling error:
The amount of imprecision in the estimate of the population parameter.
The amount added and subtracted to the point estimate to form the confidence interval.

13
Q

Determining the sample size for the mean

A

To determine the required sample size for the mean, you must know:
The desired level of confidence (1 - ), which determines the critical Z value.
The acceptable sampling error, e.
The standard deviation, σ.

14
Q

Rule for rounding confidence intervals

A

Always round up (sideways)

15
Q

If σ is Unknown

A

If unknown, σ can be estimated:
From past data using that data’s standard deviation.
If population is normal, range is approx. 6σ so we can estimate σ by dividing the range by 6.
Conduct a pilot study and estimate σ with the sample standard deviation, s.

16
Q

Determining Sample Size for the proportion

A

To determine the required sample size for the proportion, you must know:
The desired level of confidence (1 - alpha), which determines the critical Z value.
The acceptable sampling error, e.
The true proportion of ‘successes’, pi.
can be estimated with past data, a pilot sample, or conservatively use pi = 0.5.

17
Q

PHOTO 1

A

Relationship to point estimate

18
Q

PHOTO 2

A

Point estimates

19
Q

PHOTO 3

A

Estimation process

20
Q

PHOTO 4

A

Confidence interval formula

21
Q

PHOTO 5

A

Types of confidence intervals

22
Q

PHOTO 6

A

Confidence interval formula when sigma is known

23
Q

PHOTO 7

A

finding the critical z value

24
Q

PHOTO 9

A

Common levels of confidence

25
Q

PHOTOS 10-11

A

Example when sigma is known

26
Q

PHOTO 12

A

When sigma is unknown

27
Q

PHOTO 13

A

DEGREES OF FREEDOM

28
Q

PHOTO 14

A

T-TABLE

29
Q

PHOTOS 15-16

A

EXAMPLE WHEN SIGMA IS UNKNOWN

30
Q

PHOTO 17

A

INTERVALS FOR PI

31
Q

PHOTO 18

A

INTERVAL FORMULA FOR PI

32
Q

PHOTOS 19-20

A

PI EXAMPLE

33
Q

PHOTO 21

A

PI INTERPRETATION

34
Q

PHOTOS 22-23

A

DETERMINING SAMPLE SIZE FOR THE MEAN

35
Q

PHOTO 24

A

DETERMINGING SAMPLE SIZE FOR THE MEAN

36
Q

PHOTO 25

A

DETERMINING SAMPLE SIZE FOR THE PROPORTION

37
Q

PHOTO 26

A

DETERMINIGN SAMPLE SIZE FOR THE PROPORTION EXAMPLE