A research article states that y = satisfaction with police (measured using a survey questionnaire) is related to x = neighborhood social disorder (vandalism, traffic, decayed buildings and streets,...

A research article states that y = satisfaction with police (measured using a survey questionnaire) is related to x = neighborhood social disorder (vandalism, traffic, decayed buildings and streets, etc.). They summarize their findings as

Satisfaction with police declines swiftly as perceptions of neighborhood social disorder increase (n = 178; β^₁
= - 0:62; r²
= 0:18).

(a) Calculate the F test for a linear relationship between the two variables. Are the authors justified in claiming the two are related?

(b) Give a 95% confidence interval for the true value of β₁. What allows the authors to use the word “declines” in their statement?