Chapter 9: Hypothesis Testing with One Sample

population parameter

The ________ is p. The estimated value (point estimate) for p is pˆ.

Alternative Hypothesis

________ (Ha): A statement that we are trying to find evidence to support; contradictory to H0.

Null Hypothesis

________ (H0): A statement of no change, no effect, or no difference.

test statistic

The ________: Measures the difference between the sample result and the null value.

Hypothesis

________: a statement (or claim) about a property /characteristic of a population.

P value ≤ α

________: we reject the null hypothesis.

alternative hypothesis

Statistically significant: used to describe the results when the researcher has decided that the p- value is small enough to decide in favor of the ________.

sample size

Pˆ= x /n where x is the number of successes and n is the ________.

Hypothesis

a statement (or claim) about a property/characteristic of a population

Hypothesis testing

a procedure, based on sample evidence and probability, for testing claims about a property/characteristic of a population

Null Hypothesis (H0)

A statement of no change, no effect, or no difference

Alternative Hypothesis (Ha)

A statement that we are trying to find evidence to support; contradictory to H0

α

P(Type I Error) = P(Rejecting H0 when H0 is true)

β

P(Type II Error) = P(Failing to Reject H0 when H0 is false)

Power

probability we correctly reject the null hypothesis, which occurs with probability 1 − β

Type I error

We reject the null hypothesis when the null hypothesis is true

Type II error

We do not reject the null hypothesis when the alternative hypothesis is true

If you are testing a single population mean, the distribution for the test is for means

X ∼ tdf

The test statistic

Measures the difference between the sample result and the null value

p-value

the probability that, if the null hypothesis is true, the results from another randomly selected sample will be as extreme or more extreme as the results obtained from the given sample

Large p-value

calculated from the data indicates that we should not reject the null hypothesis

Smaller the p-value

the more unlikely the outcome, and the stronger the evidence is against the null hypothesis

Test statistic for a single mean

t = x¯− µ / s/ √n

Level of significance

We do this by comparing the p-value to a designated standard

For a less than an alternative hypothesis

find the probability that the test statistic z could have been equal to or less than what it is

For a greater than alternative hypothesis

find the probability that the test statistic z could have been equal to or greater than what it is

For a two-tailed alternative hypothesis

the p-value includes the probability areas in both extremes of the distribution of the test statistic z

Critical region, or rejection region

is the region of possible values for the test statistic that would lead to rejection of the null hypothesis

Critical value

A boundary of a rejection region

p-value ≤ α

we reject the null hypothesis

p-value > α

we fail to reject the null hypothesis

Statistically significant

used to describe the results when the researcher has decided that the p-value is small enough to decide in favor of the alternative hypothesis

If you Reject H0

There is sufficient evidence to conclude [statement in Ha]

If you Fail to Reject H0

There is not sufficient evidence to conclude [statement in Ha]