Hypothesis test for Difference Between Means (unpaired)

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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

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

3- Analyze: find the TS and its associated P-value for a t-test

SE: s1= SD of sample 1s2= SD of sample 2n1= sample size of sample 1n2= 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