Question

Scenario for 2-5: Research question: Is there a difference in the infant mortality rates of states above and below the mean income? Use the SPSS output below. Test the mean difference and the assumption of equal variances at the .05 level. Group Statistics N INCGROUP INFMORT Infant mortalit 1.00 below mean rate (per 1000 live births) 2.00 above mear 28 23 Mean 7.9464 6.7435 Std. Deviation 2.0224 1.1878 Std. Error Mean .3822 2477 Lovene's Test for Equality of Variances t-test for Equality of Sin Mean Deference 95% confidence Interval of the Difference Lower Upper 2421 2.1638 Std. Error Difference dr INFORhiant mort rate per 1000 live births) Sig (2-tailed .016 5.711 010 2.516 49 1.2030 Equal variances assumed Equal variances not 2.641 44.752 011 1.2030 2355 2.1204 The Levene's test in the printout indicates that the variances were not significantly different. variances were significantly different. O means were not significantly different. means were significantly different.

Answer 1

Since levene's test is used to homogeneity of variance. Therefore in levene's test our Hypothesis are:

• Null Hypothesis (H_o) : σ₁² = σ₂² i.e., population variance of two groups are equal
• Alternative Hypothesis (H₁) : σ₁² ≠ σ₂² i.e., population variance of two groups are not equal.

Now since in the test our sig. value is 0.018 which is less than 0.05 (level of significance, alpha). So we may reject our null hypothesis and conclude that "variances aresignificantly different".