aka Researcher hypothesis

The hypothesis that the researcher is trying to show. Can be one-sided or two-sided.

p ± margin of error

A type of statistical inference. Gives a range of plausible values for a parameter where we are a certain percent confident the parameter occurs. Based on sample data. There is a trade-off between confidence level and margin of error.

aka Nonparametric procedure

Does not require a normal distribution.

We reject the null hypothesis if there is significant evidence against it. 

1. Formulate a null hypothesis and alternative hypothesis, not based on research data.

2. Calculate an appropriate test statistic (z or t), based on research data.

3. Assess the significance of the test statistic to determine significance of evidence against the null hypothesis.

aka Bound on error

aka Error bound

The distance on either side of p that forms the confidence interval. Maximum error of estimate. 

aka Status quo hypothesis

The hypothesis of no effect. No difference.

aka One-tailed test

An alternative hypothesis used in a z or t test used when there is an interest to only one side of μ. P-value is the area to the left of z or to the right of z.

μ < μ₀

or

μ > μ₀

The probability of getting the observed value of the test statistic or a more extreme value, if the null hypothesis is true. The smaller the p-value, the stronger the evidence against the null hypothesis. The null hypothesis is rejected if the p value is ≤ α. If the null hypothesis is true, the distribution of the p-value is uniform between 0 and 1. If the null hypothesis is false, the distribution tends towards 0. The tendency towards 0 depends on sample size, magnitude of difference between hypothesized and true mean, and variance.

p < 0.01 : Very strong evidence against H₀

0.01 < p < 0.05 : Strong evidence against H₀

0.05 < p < 0.1 : Some weak evidence against H₀

0.1 < p < 0.2 : Litter or no evidence against H₀

p > 0.2 : No evidence against H₀

Power = 1 - β

The probability of rejecting the null hypothesis, given that it is false. Increases as α increases, as n increases, as σ decreases, and as the true value of μ is farther from μ₀.

The probability distribution of a statistic in all possible samples. μ stays the same; but σ is smaller, according to the equation 

σ_X-bar = (σ/√n)

α = P(type I error | H₀ is true)

The probability that the null hypothesis is true. Usually chosen to be 0.05. The probability of a type I error. It has a trade-off with β. Related to confidence level.

SE(X-bar) = s / √n

Because σ is unknown, SE(X-bar) is the estimate of the standard deviation of a sample. Used in a t test. 

aka Student's t distribution

Has heavier tails and a lower peak than the standard normal distribution. Measured in degrees of freedom. As degrees of freedom increases, the t distribution tends towards the standard normal distribution. Infinite degrees of freedom is the  standard normal distribution.

Used when σ is known. Works well if n > 40. Does not work well if n < 15. Same as a z-test, but uses a t distribution.

t = (x-bar - μ₀) / (s/√n)

If the null hypothesis is true, z will have normal distribution.

If the null hypothesis is true, t will have a t distribution of n - 1 degrees of freedom.

aka Two-tailed test

An alternative hypothesis used in a z test. P-value is the area to the left of -z and to the right of +z.

μ ≠ μ₀

Used when σ is known. This is a rare occurrance. Must be normally distributed population.

z = x-bar - μ₀ / (σ / √n)