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Point estimate

 a single statistic used to estimate a population parameter

Population parameters

examples are the population mean or µ, and the population standard deviation or σ.

Sample statistics

examples are the sample mean or x̄, and the sample standard deviation or s.

Sampling error

the *difference* between a sample statistic and its corresponding population parameter.

Sampling distribution of the Sample Mean

a probability distribution of all possible sample means of a given sample size.​

Central Limit Theorem

If all samples of a particular size are selected from any population, the sampling distribution of the sample mean is approximately a normal distribution.

The Standard Deviation of the Sampling Distribution of the Sample Means

It is also known as the **standard error** of the mean

Ninety-five percent (95%)

1\.96

Ninety-nine percent (99%)

2\.58

Degrees of freedom

number of values in the final calculation of a statistic that are free to vary.

Inferential statistics

Helps make estimates about a population based on a sample.​

Hypothesis

idea, suggestion, put forward as a starting-point for reasoning or explanation. ​

Hypothesis testing

a procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement.​

Null hypothesis

a statement about the value of a population parameter. (denoted by H0)

Alternate hypothesis

a statement that is accepted if the sample data provides sufficient evidence that the null hypothesis is false. (denoted by Ha)

Type I error

rejecting the null hypothesis, when it is true. (α)

Type II error

accepting the null hypothesis, when it is false. (β)

Test statistic

is a value, determined from sample information, used to determine whether to reject the null hypothesis.

Level of Significance

 is the probability of rejecting the null hypothesis when it is true.

Critical value

the dividing point between the region where the null hypothesis is rejected and the region where it is not rejected. 

Use a one-tailed test

if the alternate hypothesis, Ha, shows a direction either (< or >).

Use a two-tailed test

if the alternate hypothesis, Ha, does not show a direction, but shows the “not equal to” sign (≠).

When to use the z-statistic:

1. The sample size n is at least 30 or n ≥ 30.
2. The population standard deviation σ is given even though the sample size is small or n < 30.

When to use a t-statistic:

1. When the sample size n is less than 30 or n < 30.
2. When the population standard deviation σ is unknown.

 To know if the null hypothesis will be rejected or not

just **COMPARE** the value of your ***z or t statistic to your critical values.***

Correlation

**“Correlation rather than causation” involves the relationship between two or more variables. “CORRELATION does not imply ​causation​ “**

Independent variable

x (predictor)

Dependent variable

y (criterion)

Linear relationship

one in which relationship can be most accurately represented by a straight line.​

Positive relationship

indicates that there is ​an direct relationship between the variables.​ ( / )

Negative relationship

indicates that there is ​an inverse relationship between the variables.​ ( \\ )

Perfect relationship

is one in which a positive or negative relationship exists and all the points fall on the line.

Imperfect relationship

is one in which a relationship exists, but all of the points do not fall on the line.​

Breast cancer

Dependent variable y (criterion)

High fat diet

Independent variable x (predictor)

Children Accident Rate

Dependent variable y (criterion)

Ice cream consumption

Independent variable x (predictor)

light exposure

Independent variable x (predictor)

Plant growth

Dependent variable y (criterion)

Human birth rate

Dependent variable y (criterion)

Number of storks

Independent variable x (predictor) ( spurious)

is t - distribution?

more spread out and flatter