In: Statistics and Probability
1)
The following data represent the level of happiness and level of health for a random sample of individuals from the General Social Survey. A researcher wants to determine if health and happiness level are related. Use the αα = 0.05 level of significance to test the claim.
Health
Excellent | Good | Fair | Poor | |
Very Happy | 271 | 261 | 82 | 20 |
Pretty Happy | 247 | 567 | 231 | 53 |
Not Too Happy | 33 | 103 | 92 | 36 |
*Source: General Social Survey
1) Determine the null and alternative hypotheses. Select the correct pair.
2) Determine the test Statistic. Round your answer to two decimals.
χ2χ2 =
3) Determine the p-value. Round your answer to four decimals.
p-value =
4) Make a decision.
5) Pick a conclusion.
2) This problem demonstrates a possible (though rare) situation that can occur with group comparisons. The groups are sections and the dependent variable is an examS score.
Section 1 | Section 2 | Section 3 |
---|---|---|
60.7 | 65.6 | 56.4 |
44 | 50.1 | 49.3 |
66.4 | 25.9 | 57 |
57.9 | 44.9 | 55.6 |
62.7 | 39.1 | 52.5 |
57 | 62 | 47.3 |
52.1 | 47.3 | 63 |
49 | 23.3 | 60.5 |
50.1 | 40 | 45.6 |
Run a one-way ANOVA (fixed effect) with α=0.05α=0.05. Round the
F-ratio to three decimal places and the p-value to four
decimal places. Assume all population and ANOVA requirements are
met.
F=F=
p=p=
What is the conclusion from the ANOVA?