A survey conducted at a midwestern university and involving 1 comma 000 students found that 67​% had taken out a student loan to help pay for the cost of their college education. A similar study at a southeastern university in which 2 comma 000 students were surveyed found that 48​% had taken out a student loan.
a. Develop and interpret a 95​% confidence interval estimate for the difference in the proportions of students who have loans at these two universities.
b. Using an alpha level of 0.05​, test the hypothesis that there is no difference in the proportions of students at these two universities who have loans. How does this test compare with the result you found in part​ a?
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Part 1
a. Let p 1 be the population proportion from the midwestern university and let p 2 be the population proportion from the southeastern university. What is the 95​% confidence​ interval?
  
enter your response hereless than or equalsleft parenthesis p 1 minus p 2 right parenthesisless than or equals
  
enter your response here
​(Round to three decimal places as​ needed.)