Question 1 - One-sample t-test Food expenditure 196 Food expenditure -2.207 One-Sample Statistics N Mean 116.42 Std. Deviation 54.419 Std. Error Mean 3.887 One-Sample Test Test Value = 125 t df 195 Sig. (2- tailed) .028 Mean Difference -8.579 95% Confidence Interval of the Difference Lower -16.25 Upper -. 91 Figure 1. Output tables for Food expenditure one-sample t-test An economist predicted that the average food expenditure in Australia has changed from $125.00 per week in 2010. In a random sample of 196 Australians, the average amount spent on food was $116.42 (s= $54.42). This is lower than $125.00 per week, in which a one-sample t-test shows this difference in mean food expenditure per week is significant, t(195) = 2.21, p = 0.028 The 95% confidence interval shows that the average food expenditure for Australians is between $0.91 and $16.25 less per week than what it was in 2010. As expected, the weekly average food expenditure in Australia has changed since 2010, with Australians spending an average that is less than $125.00 on food per week. Question 2 - Independent samples t-test
Group Statistics Std. Error Mean Do you play sport? N eisureSpend yes 64 no 113 Mean 100.80 91.53 Std. Deviation 31.854 36.087 3.982 3.395 Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means F Sig. 1.934 .166 t 1.711 df 175 Sig. (2- tailed) .089 eisureSpend Equal variances assumed Equal variances not assumed 1.771 144.832 .079 Mean Difference 9.266 9.266 Std. Error Difference 5.417 5.232 Figure 2: Output tables for Leisure expenditure independent sample t-test 95% Confidence Interval of the Difference Lower Upper -1.424 19.956 -1.076 19.608 An economist hypothesised that Australian adults who play sports spend more money per week on leisure activities than those who do not play sports. For a random sample of 177 Australian adults, the average leisure expenditure per week of people who play sports (M=100.8, s=31.85, n=64) was higher than the average leisure expenditure per week of people who do not play sports (M=91.53, s=36.09, n=113). An independent samples t-test shows this difference in mean leisure expenditure per week is not significant, t(175)=1.71, p =. 089. The 95% confidence interval shows that the average leisure expenditure per week of people who play sports is between $1.42 per week lower and $19.96 per week more than people who do not play sports. There is insufficient evidence to suggest the average leisure expenditure per week on leisure activities is different for Australian adults who do play sports and do not play sports. Assumptions:
- The assumption of independence of observations has been met. - The sample used was a random sample of Australian adults. - The assumption of normality has been met. - The distribution of Leisure expenditure was approximately normal for those who play sports. - The distribution of Leisure expenditure was approximately normal for those who do not play sports. - The assumption of homogeneity of variances has been met. - The Levene's test was not significant.