Hypothesis Testing

What is the purpose of inferential statistics?

To use sample statistics to infer population parameters.

What is the first step in hypothesis testing?

State a hypothesis about a population.

What is the critical region in hypothesis testing?

It contains extreme sample values that are unlikely to be obtained if H0 is true.

What is the formula for calculating the z-score in hypothesis testing?

z = (M - μ) / (σ / √n)

What does Cohen's d measure?

The effect size, or the magnitude of an effect due to treatment or manipulation.

What is the relationship between effect size and statistical significance?

Statistical significance does not imply a large effect size.

What is the power of a statistical test?

The probability that a test will detect a real effect if there is one.

What is the generally accepted power level for hypothesis testing?

0.80

What does a one-tailed hypothesis test specify?

An effect in a particular direction, such as an increase or decrease in the population mean.

What is the effect size classification for Cohen's d when 0 < d < 0.2?

Small effect size.

What is the effect size classification for Cohen's d when 0.2 < d < 0.8?

Medium effect size.

What is the effect size classification for Cohen's d when d > 0.8?

Large effect size.

What is the first step in calculating power?

Sketch the distributions for the null and alternative hypotheses.

What is the significance of the critical region in hypothesis testing?

It helps determine whether to reject or fail to reject the null hypothesis based on sample data.

How do you determine the critical value for the sample mean?

By locating the critical region and determining the critical value for M.

What does the standard error represent in hypothesis testing?

The standard deviation of the sampling distribution of the sample mean.

What is the expected mean of ultramarathon runners if H0 is true?

μ heart rate for ultramarathon runners = 70 bpm.

What happens if the z-score falls within the critical range?

We reject the null hypothesis (H0).

What is the probability of making a Type I error denoted as?

α (alpha).

What is the probability of making a Type II error denoted as?

β (beta).

What is the significance of random sampling in hypothesis testing?

It ensures that the sample is representative of the population.

if alpha is .05 what is z

+-1.96

if alpha is .01 what is z

+- 2.58

when are one-tailed hypothesis test used

Used when the hypotheses H0 and H1 specify an effect in a particular direction

what are the Critical z-scores for 1-tailed tests

If α = .05, z = +1.65 or -1.65 and If α = .01, z = +2.33 or -2.33

what does effect size measure

measures the magnitude of an effect due to treatment, experimental manipulation, etc.