week 3 Sampling distributions and Hypothesis testing

Question 1

Sampling Error

Answer 1

Variability due to chance. Amount of deviation between a sample mean and a population mean. The Sampling Error is a concept.

Question 2

Sampling distributions

Answer 2

identifies the degree of variability between samples. The more random samples drawn, the closer the sample means will approximate a normal distribution (if is normally distributed).

n.b. “Distribution” refers to the set of values obtained from any set of observations, whereas “Sampling distribution” is reserved for the distribution of outcomes of a sample statistic.

An example of a sample distribution is if have many samples, and a mean for each. And if we plot all the sample means, we will generate a sampling distribution.

Question 3

Standard Error

Answer 3

Standard error=the standard deviation of a set of means. The degree to which a sample mean varies from the population mean. Standard error=S/ (square root of N)

where S here is the standard deviation of a set of means

Note that larger samples have less standard error than smaller ones.

The Standard Error can be calculated to estimate how much difference we might expect between a sample and population mean, purely due to chance. The Standard Error is a precise calculation.

Question 4

Hypothesis testing

Answer 4

Use sample distribution of the mean to test whether there is a statistically significant difference between the sample mean and the population mean.

A hypothesis test either tells us if there is a significant difference or not, or, whether a relationship is reliable.

Question 5

Null Hypothesis

Answer 5

H_o

The null hypothesis states that there is no satistically significant difference between groups or sample mean and population mean. Assess data and determine if we reject the null hypothesis or if we fail to reject the null hypothesis.

Question 6

Null hypothesis decision using Z-score

Answer 6

Only applicable for a normal distribution.

1. Convert to z-score.
2. consult table, when z=… smaller portion table tells us…
3. At alpha level 0.05, if smaller portion value is =/< 0.05, then the null hypothesis is rejected.

Question 7

rejection level

Answer 7

if set alpha or rejection level at 0.05 then this means there is a 5% degree of error. This is the probability of saying there is a difference, when in fact there is not.

Standardly, a one-tail test is to reject or accept at one tail of the distribution, and has alpha of 0.05. A direction is predicted in a one-tail test hypothesis eg there will be a higher than population mean in the sample mean, due to….

A 2-tail test does not predict direction, merely that there is a difference. But if we set alpha at 0.05 at both ends of a normal distribution, this results in a total of 0.1 error or 10% which is considered to gtreat. Therefore normally set 0.025 rejection at each end of the test.

ie usually if p= 0.05, the null hypothesis is rejected.

Question 8

Type 1 error

Answer 8

when we erroneously reject the null hypothesis. (controlled by where we set rejection level)

Question 9

Type 2 Error

Answer 9

When we fail to reject the null hypothesis and the null hypothesis is false (ie it should be rejected).

This relates to how powerful the hypothesis testing is.