Reject the null hypothesis Conclusion? Recall the claim was that at least one state was different than the others (alternative hypothesis). Since we rejected the null, we support this claim. Our P-value is very small and our test statistic very large, so we have significant sample evidence. Conclusion: There is significant sample evidence to support the claim that the mean average salaries of people in Northern Territory, New South Wales, Queensland, Victoria, and Tasmania are different. Assumptions for ANOVA Random Sample sizes at least 30 or bell shaped Groups Independent of each other Equal population variances (no group has a standard deviation more than twice as big as any other group) Check the assumptions for the Australian states problem. Random? The data was a random sample of people living in these states in Australia. 30 or bell shaped? Some histograms were bell shaped and some a little skewed, but since the sample sizes were 35 (over 30), it does pass this assumption. Independent groups? The data may fail this one. Salaries from state to state all may be related due to their reliance on the overall economy and unemployment rates of Australia. Equal Population Variances? Looking at the standard deviations listed in the ANOVA printout. The larges standard deviation is 701.5 and the smallest was 386.4, so no standard deviation was more than twice as large as any other. So it passes this assumption.
Reject the null hypothesis Conclusion? Recall the claim was that at least one state was different than the others (alternative hypothesis). Since we rejected the null, we support this claim. Our P-value is very small and our test statistic very large, so we have significant sample evidence. Conclusion: There is significant sample evidence to support the claim that the mean average salaries of people in Northern Territory, New South Wales, Queensland, Victoria, and Tasmania are different. Assumptions for ANOVA Random Sample sizes at least 30 or bell shaped Groups Independent of each other Equal population variances (no group has a standard deviation more than twice as big as any other group) Check the assumptions for the Australian states problem. Random? The data was a random sample of people living in these states in Australia. 30 or bell shaped? Some histograms were bell shaped and some a little skewed, but since the sample sizes were 35 (over 30), it does pass this assumption. Independent groups? The data may fail this one. Salaries from state to state all may be related due to their reliance on the overall economy and unemployment rates of Australia. Equal Population Variances? Looking at the standard deviations listed in the ANOVA printout. The larges standard deviation is 701.5 and the smallest was 386.4, so no standard deviation was more than twice as large as any other. So it passes this assumption.