Module 7, Confidence Intervals

Question 1

Confidence Level:

Answer 1

how likely our parameter is to lie within that interval ^^;

Question 1

Margin of Error:

Answer 1

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

Question 2

Why is a confidence interval inferential?

Answer 2

An inferential stat because sample stats are used to estimate the location of population parameters (GENERALIZING)

Question 3

Point vs. interval estimate

Answer 3

Point Estimate: single statistic that is used as our best estimate of a corresponding parameter (the value in a population from which you drew that estimate), GREATER PRECISION, LESS ACCURACY (very specific single stat)
Have extensive precision: give us a specific figure
DISADVANTAGE OF POINT ESTIMATE: low accuracy, low freedom from error/the extent to which our estimate differs from the parameter of interest’s true value
Interval Estimate: provides us with a RANGE of values within which the population parameter is likely to fall; GREATER ACCURACY, LESS PRECISION, this range is more accurate but not precise because of how the big the range can be

Question 4

Sampling Theory and level of Confidence

Answer 4

Sampling Theory: a well-drawn probability sample, where every element has a known probability of being selected, normally involving a random mechanism, will yield results that closely resemble those we would get if we measured the ENTIRE population

Question 5

Law of Large Numbers:

Answer 5

states that with a sufficiently large sample size, sample statistics (usually means) will tend to approximate population parameters very closely (THEY SHOULD BE VERY SIMILIAR

Question 6

Confidence Level:

Answer 6

specifies the probability that our particular sample’s interval estimate will contain the population parameter

Question 7

95% Confidence Level:

Answer 7

if a large number of samples is collected and a confidence interval is created for each sample, approximately 95% of these intervals will contain the population mean

Question 8

Confidence interval vs. confidence level

Answer 8

Confidence Interval: range of values within which we estimate that a population parameter will fall (LOWER BOUND AND UPPER BOUND OF AN INTERVAL WITHIN WHICH WE ESTIMATE A POPULATION PARAMETER WILL FALL, IE. MEAN NUMBER OF FRIENDS IS BETWEEN 200-240)
Confidence Level: specifies the PROBABILITY that the population parameter will lie within that specified range of values

Question 9

What does a higher level of confidence mean?

Answer 9

HIGHER LEVEL OF CONFIDENCE = WIDER THE CONFIDENCE INTERVAL
LOWER LEVELS OF CONFIDENCE: HAVE A SMALLER INTERVAL BECAUSE THE TRADE OFF FOR HAVING A SMALLER AND MORE PRECISE RANGE OF VALUES IN WHICH WE THINK OUR PARAMETER LIES IS THAT WE CAN BE LESS SURE THAT WE WOULD CAPTURE IT IN SUBSEQUENT SAMPLES

Question 10

Sampling error vs. margin of error

Answer 10

Sampling Error: we can reasonably assume that there will always be at least some gap between our sample statistics and their respective population parameters
Margin of Error:m estimate of the AMOUNT OF DIFFERENCE that we think is possible between our statistic and its corresponding parameter

Question 11

Sampling theory and sample size

Answer 11

SAMPLING THEORY: the larger the sample size, the LESS amount of sampling error we expect there to be = smaller margin of error (to know if this is true, we would need to know the population parameter)

Question 12

CLT

Answer 12

states that with repeated samples, the sampling distribution will eventually become approximately normal and the mean of all samples will approximate the mean of the population

Question 13

CLT and increasing sample size

Answer 13

INCREASING SAMPLE SIZE: HAS THE SAME EFFECT AS REPEATING SAMPLES OVER AND OVER AGAIN, IT REDUCES THE MARGIN OF ERROR
AS SAMPLE SIZE INCREASES, THE MARGIN OF ERROR VALUE BECOMES SMALLER AND THE CONFIDENCE INTERVAL BECOMES MORE NARROW

Question 14

Two assumptions when using confidence intervals

Answer 14

First assumption: is that you have used simple random sampling
Second assumption: is that we have a normal probability distribution; this is crucial because confidence intervals rely on the Central Limit Theorum in order to make an interval estimate

Question 15

When to use t-distribution?

Answer 15

Developed the t-distribution when normal distribution cannot work on small sample sizes: frequency distribution of standard deviations of samples drawn from a normal population

Question 16

Properties of T-distribution

Answer 16

Unimodal and symmetrical about the mean
Tend to be flatter and with thicker tails than the norm distribution
Identified by degrees of freedom associated with them
Mean of 0 and SD is greater than 1
Value of the t-statistic ranges from negative to positive infinity
Shape is dependent on sample size
AS SAMPLE SIZE INCREASES: THE SHAPE APPROACHES THAT OF THE STANDARD NORMAL DISTRIBTUION
When df (DEGREES OF FREEDOM)=infinity, the T-distribution exactly matches the standard normal distribution

Question 17

Degrees of Freedom:

Answer 17

the amount the final calculations are allowed to vary; equal to the sample size minus 1
Degrees of freedom are generally equal to the number of observations we used to estimate the parameter minus the number of intermediate parameters we need to estimate

Question 18

Effect of sample size on t-distribution

Answer 18

As sample size increases, the t-distributions BECOMES MORE NORMAL
N is equal to or greater than 30, the sampling distribution so closely approximates the normal distribution, that we could use the normal distribution instead
^^THIS IS BECAUSE OF THE CENTRAL LIMIT THEORUM: AS SAMPLE SIZE INCREASES DISTRIBUTION BECOMES MORE NORMAL

Question 19

When are t vs. z stats used?

Answer 19

T-Statistics are used for comparisons when n<30, and z-stattistics can be used when n is > or equal to 30

Question 20

Standardized Test Statistic:

Answer 20

enables you to take a score from a sample and transform it into a standardized form very similiar to a z-score

Question 21

Why is a smaller confidence interval better?

Answer 21

more accurate; A large confidence interval suggests that the sample does not provide a precise representation of the population mean, whereas a narrow confidence interval demonstrates a greater degree of precision.

Question 22

Effects of n increasing on Confidence level

Answer 22

confidence level increases as n increases

Question 23

Basic principles of confidence intervals

Answer 23

As n increases, so does confidence level
As n increases, confidence interval becomes more precise and becomes narrower
The narrower the CI, the better and more precise
As confidence level increases, confidence interval increases and becomes less precise
As n increases, the maximum possible distance our stat is from the population parameter decreases, which means the confidence interval becomes narrower and more precise

Question 24

C

Answer 24

area under the standard normal curve between the critical values

Question 25

What effect does increasing degrees of freedom have on the t-distribution?

Answer 25

after 29df, the t distribution is very close to the standard normal distribution
GREATER DF=CLOSER TO NORMAL

Question 26

Relationship between df and t

Answer 26

Inverse; as t increases, degree of freedoms decrease
As t decreases, degree of freedom increases