- Complete a two-sample [latex]t[/latex]-test for independent population means from hypotheses to conclusions
Test Statistics
[latex]t[/latex] – statistic
The test statistic to compare two population means is calculated using the following formula:
[latex]t = \dfrac{\text{estimate of parameter - null hypothesis value}}{\text{standard error}} = \dfrac{(\bar{x}_1-\bar{x}_2)-(\mu_1-\mu_2)}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}[/latex]
The summary for the Hate Crime set can be seen below:
| Group 1: Year 2019 | Group 2: Year 2020 | |
| Sample Mean | [latex]\bar{x}_1 =2.36[/latex] | [latex]\bar{x}_2 =3.13[/latex] |
| Sample Standard Deviation | [latex]s_1 =1.79[/latex] | [latex]s_2 =2.04[/latex] |
| Sample Size | [latex]n_1 =47[/latex] | [latex]n_2 =47[/latex] |
Let’s conduct the hypothesis test using the statistical tool below.
Step 2: Edit the Group Label accordingly
Step 3: Enter the statistics into the statistical tool
Step 4: Select “Significance Test” for the “Type of Inference”
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We often learn more from constructing confidence intervals than from the hypothesis test because it shows a range of plausible values for the difference between the population means.