This document outlines the steps for conducting a hypothesis test comparing the means of two independent samples. The test assumes simple random sampling, independent samples that are much larger than the sample sizes, and approximately normally distributed sampling distributions. The steps are: 1) state the null and alternative hypotheses, 2) choose a two-sample t-test analysis, 3) calculate the t-statistic and p-value, 4) compare the p-value to the significance level and reject or fail to reject the null hypothesis.

1. Hypothesis test for
Difference Between
Means (unpaired)

2. •

3. •

5. Conditions
• Simple random Sample
• The samples are independent
• Each population is at least 10 times larger
than each sample size
• The sampling distribution is approximately
normally distributed

6. Conducting a Hypothesis test
1- state the hypothesis: Ho & Ha (mutually exclusive)
*when the null hypothesis states there is no difference between
the 2 population proportions (d=0), and it is a two tail test, then :
Ho: μ1= μ2 & Ha: μ 1 = μ2
2- Analysis Plan
* Test Method: use a 2 sample t- test to determine whether
the hypothesized difference between the population means differs
significantly from the observed sample difference

7. 3- Analyze: find the TS and its associated P-value for a t-test
SE: s1= SD of sample 1
s2= SD of sample 2
n1= sample size of sample 1
n2= sample size of sample 2
**DF would be smaller of: n1-1 or n2-1
*TS: t = (x1-x2) x1= mean of sample 1
SE x2= mean of sample 2
*P-value- probability of observing a sample statistic as extreme as the TS
(where the TS is a t-score)
4- Interpret- compare the P-value to the significance level
and reject null when the P-value is less than the
Significance level