The percentage of students from for profit institutions who have defaulted on their student loans has received much attention recently. Suppose the following data were collected from a random sample of students who graduated three years ago from various types of institutions with student loans:

a. Using α = 0.05, perform a chisquare test to determine if the proportion of students who default on their student loans differs by the type of institution.

b. Confirm your results using p_value.

c. Interpret the meaning of the p_value from p_value².

d. How does the type of institution appear to relate to the likelihood of students defaulting on their loans?

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Defaulted on Loan? Institution Public Private For-profit Yes No 143 67 13