Two Stats Questions

STAT 4202 HW 5 Due Wednesday, December 7th

1. Below is a scatterplot of the percent of voters in a state who voted for Donald Trump vs. the

obesity rate of the state according to the 2015 CDC Behavioral Risk Factor Surveillance System.

Since the data appear to be linear, a line was fit using R. Use the output beneath the scatterplot

to answer the questions below.

Sources: http://stateofobesity.org/files/stateofobesity2016.pdf, http://www.politico.com/2016-

election/results/map/president (retrieved 2 Dec 2016)

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) -5.1435 8.1924 -0.628 0.533

obesity 1.8694 0.2762 6.768 1.67e-08

Residual standard error: 7.289 on 48 degrees of freedom

Multiple R-squared: 0.4883, Adjusted R-squared: 0.4777

F-statistic: 45.81 on 1 and 48 DF, p-value: 1.666e-08

Response: trump

Df Sum Sq Mean Sq F value Pr(>F)

obesity 1 2434.3 2434.27 45.812 1.666e-08

Residuals 48 2550.5 53.14

a. Find the estimated regression line.

b. Estimate the percentage of votes for Trump in a state with an obesity rate of 22%.

c. Estimate the percentage of votes for Trump in a state with an obesity rate of 32%.

d. Interpret �̂�

e. Find a 95% CI for𝛽; interpret.

f. What does 10�̂� represent?

g. Find a 95% CI for10𝛽; interpret.

h. Test to see if there is a positive linear relationship between obesity rate and percentage of votes

for Trump.

i. Regardless of your answer to part h, if we assume there is a positive linear relationship between

obesity rate and percentage of votes for Trump does that mean a higher obesity rate in a state

causes a higher percentage of voters to vote for Trump? Why or why not?

STAT 4202 Quiz 5 Due Wednesday, December 7th

1. A study was conducted to ascertain the benefits, if any, of l-arginine on systolic blood pressure.

30 subjects were recruited and randomized to one of three arms: placebo, 1000mg/day,

2000mg/day. At the beginning of the study, there were no significant differences in the systolic

blood pressure, on average, for the three groups. The subjects took the pills for six weeks and

then their blood pressure was measured. Test to see if there is a difference in the systolic blood

pressure, on average. The data are below. Regardless of the outcome of the test find pairwise

confidences intervals for the difference in the means using the Bonferroni method with an

overall confidence level of 95%.

Placebo 1000mg/day 2000mg/day

120 115 121

105 124 112

113 118 123

125 123 110

112 126 120

119 117 122

118 112 113

126 130 118

118 121 121

125 134 117