this problem, we will analyze the effect of categorized PROP_LUNCH on the variable CRIME_RATE when accounting for PROP_CHANGE_INCOME. The researchers decided to categorize the variable PROP_LUNCH into 3 categories: Lunch A = “Neighborhoods with no more than 33% of schools participating in free school lunch program” Lunch B = Neighborhoods more than 33% but no more than 66% of schools participating in free school lunch program” Lunch C = “Neighborhoods more than 66
In this problem, we will analyze the effect of categorized PROP_LUNCH on the variable CRIME_RATE when accounting for PROP_CHANGE_INCOME. The researchers decided to categorize the variable PROP_LUNCH into 3 categories:
Lunch A = “Neighborhoods with no more than 33% of schools participating in free school lunch program”
Lunch B = Neighborhoods more than 33% but no more than 66% of schools participating in free school lunch program”
Lunch C = “Neighborhoods more than 66% of schools participating in free school lunch program”
Give the estimated model :crime_rate = 142.5737 - 1.9215(Prop_change_income) -38.8741(Lunch A) - 19.20521(Lunch B)
(1) For neighborhoods with more than 66% of schools participating in free school lunch program, the estimated regression model is:crime_rate = 142.5737 - 1.9215(Prop_change_income) - 38.8741(0) - 19.20521(0) = 142.5737 - 1.9215(Prop_change_income)
(2) For neighborhoods with 33% to 66% of schools participating in free school lunch program, the estimated regression model is:crime_rate = 142.5737 - 1.9215(Prop_change_income) - 38.8741(0) - 19.20521(1) = 123.36849 - 1.9215(Prop_change_income)
(3) For neighborhoods with less than 33% of schools participating in free school lunch program, the estimated regression model is:crime_rate = 142.5737 - 1.9215(Prop_change_income) - 38.8741(1) - 19.20521(0) = 103.69959 - 1.9215(Prop_change_income)
Question:Test whether the crime rate in neighborhoods with 33% to 66% of schools participating in free school lunch program is significantly different than the crime rate in neighborhoods with more than 66% of schools participating in free school lunch program when adjusting for percent change in household income over past several years using a t-test. Don't forget to specify the null and alternative hypothesis, test statistic, degrees of freedom, p-value, decision and conclusion in the words of the problem. Use level of significance 5%.
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