10. TESTING ONE-TAILED AND TWO-TAILED HYPOTHESES

two-tailed equation

(1-alpha)/2

z___(0.95) = 1.645 (how to find this)

- subtract 0.5 from 0.95 to get 0.45 - find that in the # of values and find the row and column that corresponds as a z-score - an alpha of 0.05 is used in a one-tailed test - 1.645 separates the regions where the null hypothesis is rejected and where it isn't - 1.645 is the critical value

level of significance (alpha)

expresses the probability of rejecting the null hypothesis when it is true - sometimes called the level of risk - can be any value between 0 and 1 - traditionally 0.05 is used for consumer research projects, 0.01 for quality assurance, and 0.1 for political polling (recommendations)

type 1 error (designated with alpha)

rejecting null hypothesis when it is true

testing a mean, std dev or sigma unknown (formula)

t = (x-bar - mean) / (s/sqrt of n)

critical value

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

p-value

the probability of observing a sample value as extreme as, or more extreme than, the value observed, given that the null hypothesis is true (strength of rejection)

testing a mean, std dev or sigma known (formula)

z = (x-bar - mean) / (sigma/sqrt of n)

type 2 error formula

z = x-bar(c) - mean(1) / sigma/sqrt of n - x-bar(c) is the confidence limit - mean(1) is an assumed true mean

test statistic

A value, determined from sample information, used to determine whether to reject the null hypothesis

mutually exclusive

events that cannot happen at the same time

z___[0.975] (how to read it)

0.975 quantile of the std norm dist

one-tailed equation

1-alpha

power of the test

1-beta (probability of not making a type II error OR that you reject the null hypothesis when it is false)

z___1-half-alpha (how to read it)

1-half alpha quantile of the standard norm dist

Steps for Hypothesis Testing

1. State null hypothesis (what we would expect) and alternate hypothesis 2. Select a level of significance (what alpha would be) 3. Identify the test statistic (can be z if std dev is known, t is std dev is unknown) 4. Formulate a decision rule (use equation) 5. Take a sample, arrive at a decision 6. Interpret result

what is the 0.975 quantile of the std norm dist

1.96 (the z score)

hypothesis testing

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

hypothesis

a statement about a population parameter subject to verification

null hypothesis (Ho)

a statement about the value of a population parameter developed for the purpose of testing numerical evidence - always includes the equal sign

alternate hypothesis (Hi)

a statement that is accepted if the sample data provide sufficient evidence that the null hypothesis is false - never includes the equal sign

type 2 error (designated with beta)

accepting null hypothesis when you should have rejected it

1-alpha confidence interval (prob that it doesn't contain pop mean)

alpha

probability of having a type 1 error

alpha

collectively exhaustive

at least one of the events must occur when an experiment is conducted

probability of having a type 2 error

beta