Lab 4: Independent Samples t-Tests
When two samples are involved, the samples can come from different individuals who are not matched (the samples are independent of each other.)
On the other hand, when the sample can come from the same individuals (the samples are paired with each other) and the samples are not independent of each other.
The Independent Samples t-test can be used to see if two means are different from each other when the two samples were taken from different individuals who have not been matched.
The denominator is the standard error of the difference between two means.
We will follow the steps:
1. Write the null (Ho) and alternative (H1) hypotheses first:
H0: µ1 = µ2 H0: µ1 = µ2 H0: µ1 = µ2
H1: µ1 ≠ µ2 H1: µ1 > µ2 H1: µ1 < µ2
Or
H0: µ1 -µ2 = 0 H0: µ1 - µ2 = 0 H0: µ1 - µ2 = 0
H1: µ1 - µ2 ≠ 0 H1: µ1 - µ2 > 0 H1: µ1 - µ2 < 0
where µ1 and µ2 is the mean number of the sample1 and sample2, respectively.
2. Determine if this is a one-tailed or a two-tailed test and specify the α-level.
3. Use Megastat to find the p-value, t-value and F-value and other parameters
4. Check the test for equality of variances and select the appropriate t-value, accordingly.
5. Plot the t-distribution and show the critical and non-critical regions, locate the p-value and state the result whether the null hypothesis Ho is rejected or not.
6. Draw a conclusion: (choose one of the following situations)
a. There is enough evidence to reject the claim that … if the claim is Ho
b. There is no enough evidence to reject the claim that … if the claim is Ho
c. There is enough evidence to support the claim that … if the claim is H1
d. There is no enough evidence to support the claim that … if the claim is H1
Remarque: (on the p-value)
The p-value is the actual area under the t distribution curve and it is equal to the probability Pr(T t) ; while is the actual area under the t distribution curve and it is equal to the probability Pr (T tvc ) .
We compare the p-value to the significance level , whether it is a two-tailed or one-tailed test, such that:
• If the p-value , reject the null hypothesis
• If the p-value > , do not reject the null hypothesis
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