2-Sample t-test

STAT>BASIC STATISTICS>2 SAMPLE t

$$H_{0}: \mu_{1} - \mu_{2} = 0$$. $$H_{0}: \mu_{1} - \mu_{2} = 0$$ If variances are assumed to be equal, then the common variance is estimated by the pooled vaiance.

Assuming equal variances

Two-Sample T-Test and CI Sample   N    Mean  StDev  SE Mean 1       10    9.63   1.20     0.38 2       15  10.780  0.940     0.24 Difference = mu (1) - mu (2) Estimate for difference:  -1.150 95% CI for difference:  (-2.036, -0.264) T-Test of difference = 0 (vs not =): T-Value = -2.68  P-Value = 0.013  DF = 23 Both use Pooled StDev = 1.0494

Using $$\alpha = 0.05$$, we would reject $$H_{0}$$ because the p-value < 0.05.

To test for equal variances use:

STAT>BASIC STATISTICS>2 VARIANCES

$$H_{0}: \sigma^{2}_{1} = \sigma^{2}_{2}$$. $$H_{1}: \sigma^{2}_{1} \neq \sigma^{2}_{2}$$

 

Using $$\alpha = 0.05$$, we would fail to reject $$H_{0}$$ because p-value > 0.05.

 

Test for Equal Variances 95% Bonferroni confidence intervals for standard deviations Sample   N     Lower    StDev    Upper      1  10  0.784948  1.20000  2.41638      2  15  0.658383  0.93808  1.59000 F-Test (Normal Distribution) Test statistic = 1.64, p-value = 0.394

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