2 Sample Hypothesis Testing

2 Sample Hypothesis Test

compares 2 parameters from 2 populations

z-Test Guidelines (proportions)

1. State the claim mathematically and identify the null and alternative hypothesis 2. specify the level of significance (alpha) 3. determine critical value(s) 4. determine rejection region(s) 5. Find the weighted estimate of p1 and p2 6. find the standardized test and sketch the sampling distribution 7. make a decision to reject or fail to reject the Ho 8. Interpret decision.

z-Testing Guidelines (large samples)

1. State the claim mathematically and identify the null and alternative hypothesis 2. specify the level of significance (alpha) 3. determine critical value(s) 4. determine rejection region(s) 5. find the standardized test and sketch the sampling distribution 6. make a decision to reject or fail to reject the Ho 7. Interpret decision.

t-Testing Guidelines (dependent samples)

1. State the claim mathematically and identify the null and alternative hypothesis 2. specify the level of significance (alpha) 3. determine the degrees of freedom 4. determine the critical value(s) 5. determine rejection region(s) 6. calculate d "bar" and sd (standard deviaton of differences) 7. find the standardized test 8. make a decision to reject or fail to reject the Ho 9. Interpret decision.

t-Testing Guidelines (small samples)

1. State the claim mathematically and identify the null and alternative hypothesis 2. specify the level of significance (alpha) 3. determine the degrees of freedom 4. determine the critical value(s) 5. determine rejection region(s) 6. find the standardized test and sketch the sampling distribution 7. make a decision to reject or fail to reject the Ho 8. Interpret decision.

t-Test (Difference btw Means)

3 condition to perform a test between the difference population means u1 and u2: 1. the sample must be randomly selected 2. the sample must be independent 3. each population must have a normal distribution test statistic: x1- x2 (sample means) sample size must be less than 30 * standard error and the degrees of freedom depend whether the population variances are equal o1=02 * when o1=02, then there is a pooled estimate of standard deviation

Z-Test (Difference btw Means)

3 condition to perform a test between the difference population means u1 and u2: 1. the sample must be randomly selected 2. the sample must be independent 3. each sample size must be at least 30, or, if not, each population must have a normal distribution with known standard deviation test statistic: x1- x2 (sample means) * ALWAYS assume that there is no difference between the population means u1= u2

z-Test (Difference btw Proportions)

3 conditions required to conduct a test between 2 population proportions, p1 and p2: 1. the sample must be randomly selected 2. the sample must be independent 3. the sample must be large enough to use a normal sampling distribution test statistic: p "hat"1- p "hat"2

t-Test (Difference btw Means) Dependent Samples

To perform a 2 sample hypothesis find the difference btw each data pair. d= x1-x2 1. the sample must be randomly selected 2. the sample must be dependent (paired) 3. each population must have a normal distribution test statistic: d "bar" (mean of the differences)

Sampling methods

a) independent samples- the sample selected from one population is not related to the sample selected from the second population b) dependent samples (paired or matched)- each member of one sample corresponds to a member of the other sample

independent sample

a) null hypothesis; a statistical hypothesis that usually states there is no difference between the parameters of two populations b) alternative hypothesis- a statistical hypothesis that is true when null hypothesis is false