Question

1. 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).

Answer 1

(a) The organized data is:

b)

Does income depend on the happiness level?

The hypothesis being tested is:

H₀: µ1 = µ2 = µ3

H_a: Not all means are not equal

c)

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.

d)

Since the p-value (0.048) is less than the significance level (0.05), we can reject the null hypothesis.

e)

Therefore, we can conclude that income depends on the happiness level.

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