Explain how outliers affect a Pearson correlation. Researchers identify that there is a significant relationship between happiness and sense of belonging. The linear regression equation for predicting happiness from sense of belonging is =3+0.5X. Using this equation, what happiness score would you expect from a person who scored a 49 on a sense of belonging scale? Professor Benjamin wanted to see if different age groups have different attention spans. To test this, Prof. Benjamin recruited 20 children from each of the 4 age groups (3 years old, 6 years old, 9 years old, and 12 years old). Below is an ANOVA summary table from Prof. Benjamin's hypothetical study. Source SS df MS F Between 50 3 16.67 F=6.44 Within 300 116 2.59 Total 350 119 Run a hypothesis test using an ANOVA and write a paragraph (or list) of responses to the following items. MAKE SURE TO LABEL EACH SECTION IN YOUR ANSWER USING A THROUGH F. (a) Hypotheses (b) Critical value ( = 0.05) (c) F ratio (d) Conclusion about the null hypothesis (e) Measure of effect size (f) Written summary of the conclusions that can be made from this study (including an interpretation of the null decision, effect size, and confidence interval) Researchers gathered data from n=7 individuals to see if income is related to attractiveness. Below is the data for that study. Income was measured in thousands of dollars attractiveness was rated on a scale from 1-10. If the Pearson correlation value is r=+0.28, is there enough evidence to say that there is a significant relationship between attractiveness and income? Use an alpha of 0.05, two-tailed test. Run a hypothesis test using a Pearson correlation and write a paragraph (or list) of responses to the following items. MAKE SURE TO LABEL EACH SECTION IN YOUR ANSWER USING A THROUGH E. (a) Hypotheses (b) Critical value ( = 0.05, two tails) (c) Conclusion about the null hypothesis (d) Measure of effect size (e) Written summary of the conclusions that can be made from this study (including an interpretation of the null decision, effect size, and confidence interval)