# T-Test for Two Independent Samples

* This test is used when only two unrelated groups are being compared and the measurements are either interval or ratio. The two groups may or may not have the same number of samples. * The t-test for two independent groups involves testing whether or not there is a significant difference between the population means of the two groups.

Consider a study wherein the effectiveness of banana leaves as an organic wrapper was compared to that of aluminum foil. The number of bacterial colonies in rice wrapped in the two kinds of food wrappers was measured after 12 hours at room temperature. Treatment| Number of Bacterial ColoniesReplicates|

| 1| 2| 3|

Banana Leaves (Experimental)| 4| 8| 7|

Aluminum Foil (Control)| 5| 3| 7|

The main steps in analyzing and interpreting the data are:

a. Set up and test the appropriate statistic.

b. Formulate and interpret your conclusion.

The appropriate test statistic is a t-test for two independent samples. The following procedure is used: 1. State the null hypothesis to be tested.

HO: μA= μB or μA- μB=0

* There is no significant difference between the numbers of bacterial colonies present in cooked rice wrapped with aluminum foil.

2. State the alternative hypothesis in symbols and in words. HO : μA ≠ μB or μA - μB ≠ 0

* There is a significant difference between the mean number of bacterial colonies present in cooked rice wrapped with banana leaves and in cooked rice wrapped with aluminum foil.

*Note the non-directionality of the HA; consequently a two-tailed test of significance is employed. 3. State the level of significance: a=0.025

Banana Leaves (Experimental) | Aluminum Foil (Control)|

X1| X12| X2| X22|

4| 16| 5| 25|

8| 64| 3| 9|

7| 49| 7| 49|

X1=19| X12=129| X2=15| X22=83|

4. Set up the following table:

5. Compute t...

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