In: Statistics and Probability
Please Perform one Chi-square Test by doing the following (Hint: Chapter 15/17, Nonparametric Methods: Chi-Square):
a. Organize the data and show in MS Excel (5 points);
b. Write down one potential question that you could answers using Chi-square test with the Happiness_2011.xls dataset and state its null and alternate hypotheses (5 points);
c. Perform one Nonparametric Methods: Chi-Square Test using any two reasonable variables from the Happiness_2011.xls dataset (two qualitative variables) and show the analysis results for the question (10 points);
d. Indicate whether you reject or accept the null hypothesis (5 points);
e. Interpret your findings from the analysis (5 points).
(a) The organized data is:
(b), (c), (d) & (e) The question to be analyzed is:
Does income depend on the happiness level?
The hypothesis being tested is:
H0: µ1 = µ2 = µ3
Ha: Not all means are not equal
Analysis of Variance
Source | DF | Adj SS | Adj MS | F-Value | P-Value |
Happiness | 2 | 145.3 | 72.65 | 3.12 | 0.048 |
Error | 98 | 2279.8 | 23.26 | ||
Total | 100 | 2425.1 |
The p-value is 0.048.
Since the p-value (0.048) is less than the significance level (0.05), we can reject the null hypothesis.
Therefore, we can conclude that income depends on the happiness level.