7.41 Murders and poverty, Part II. Exercise 7.29 presents regression output from a model for predicting annual murders per million from percentage living in poverty based on a random sample of 20 metropolitan areas. The model output is also provided below. | Estimate | Std. Error | t value | Pr(>|t|) | | (Intercept) | -29.901 | 7.789 | -3.839 | 0.001 | | poverty% | 2.559 | 0.390 | 6.562 | 0.000 | | s =5.512 | R2 = 70.52% | R2adj = 68 .89% |

(a)What are the hypotheses for evaluating whether poverty percentage is a significant predictor of murder rate? H0 = Poverty% is not a significant predictor of murder rates Ha = Poverty% is a significnat predictor of murder rates

  1. State the conclusion of the hypothesis test from part (a) in context of the data. p-value of poverty% is approximately 0 which leads us to reject the null hypothesis and conclude that there is sufficient evididence that poverty% is a significant predictor of murder rates.

  2. Calculate a 95% confidence interval for the slope of poverty percentage, and interpret it in context of the data. For each % increase in poverty we expect the murder rate, on average, to increase by 1.73964 to 3.37836.

n = 20
df = n-2
tv = 1-(0.05/2)

t <- qt(tv, df)
t
## [1] 2.100922
est = 2.559
se = 0.390

ci_low <- est-t*se
ci_upp <- est+t*se
ci_low
## [1] 1.73964
ci_upp
## [1] 3.37836
  1. Do your results from the hypothesis test and the con???dence interval agree? Explain. Yes the results agree, we rejected the null hypothesis and the confidence interval does not include 0