we have a random sample of 80 countries. For each country we recorded the overall happiness score (out of 10 points) along with the life expectancy (in years).

You are asked to provide the following two items to be included as part of a report:

• A 90% confidence interval to estimate the average increase in happiness score for every one year increase in life expectancy for all countries in the world.
• Using the resulting 90% confidence interval, is there sufficient evidence to suggest that a higher life expectancy is associated with a higher happiness score, on average. Explain why.

For which of the following countries would you expect the 90% prediction interval for the happiness score to be the widest?

a) Netherlands with a life expectancy of 72 years

b) Haiti with a life expectancy of 55.7 years

c) Ethiopia with a life expectancy of 59 years

d) Philippines with a life expectancy of 62 years

Call: 1m(formula = Happiness. score ~ Life. expectancy, data = happiness) Residuals: Min 1Q Median 3Q Max -1. 3949 -0. 5823 0. 0187 0. 5864 1.2539 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -2.5596 0. 8112 -3.16 0. 0023 *# Life. expectancy 0. 1228 0. 0123 9.95 1. 6e-15 * *# Signif. codes: 0 '*#* ' 0.001 '#* ' 0.01 '#' 0.05 ' . ' 0.1 . ' 1 Residual standard error: 0.72 on 78 degrees of freedom Multiple R-squared: 0.559, Adjusted R-squared: 0.553 F-statistic: 98.9 on 1 and 78 DF, p-value: 1.6e-15 Min 1st Qu. Median Mean 3rd Qu. Max Life Expectancy 50.83 61.66 66.70 65.39 69.66 76.82 Happiness Score 2.523 4.884 5.397 5.469 6.170 7.620