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Answer :
Final answer:
The variables useful in predicting the violent crime rate at a significance level of 0.05 are the ones with p-values less than 0.05. The 95% confidence interval for police officer wage cannot be calculated without the mean and standard deviation of the sample. The p-value of 0.069 does not imply that police officer wage is unrelated to the violent crime rate, but rather that it does not make a significant contribution to predicting the violent crime rate after including the police academy graduation rate in the model.
Explanation:
a) Which variables are useful in predicting violent crime rate, for α = 0.05?
In order to determine which variables are useful in predicting the violent crime rate, we need to look at the p-values associated with each variable in the regression model. If the p-value is less than the significance level (α = 0.05), then the variable is considered statistically significant and useful in predicting the violent crime rate.
b) Compute the 95% confidence interval for police officer wage:
A 95% confidence interval provides a range of values within which we can be 95% confident that the true population parameter lies. To calculate the confidence interval for police officer wage, we need the mean and standard deviation of the sample. Unfortunately, these values are not provided in the given information.
c) Does the p-value of 0.069 imply that police officer wage is unrelated to violent crime rate?
The p-value of 0.069 is greater than the significance level (α = 0.05), which means that we fail to reject the null hypothesis. This implies that there is not enough evidence to conclude that police officer wage is statistically significant in predicting the violent crime rate. However, it does not necessarily mean that police officer wage is unrelated to the violent crime rate. It simply means that it does not make a significant contribution to predicting the violent crime rate after including the police academy graduation rate in the model.
Learn more about regression analysis and significance testing here:
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