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# Chi square goodness of fit test

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A large banking corporation believes that 80% of the loan applications it receives are approved within 24 hours. It decides to take a random sample of 10 loan applications every day for 3 months and record the number of the applications that are approved within 24 hours. The following data are obtained:

Number of Loan Applications in 10 Approved in 24 Hours Frequency
4 1
5 5
6 11
7 19
8 27
9 18
10 7
Total 88

a). Set up the necessary hypotheses to test whether the data come from a binomial distribution with n = 10 and p = 0.80.
b). Find the expected frequency distribution for the data.

c). A the 0.05 level of significance, is it reasonable to assume that the number of loan applications that are approved in 24 hours has a binomial distribution with p= 0.80.

##### Solution Summary

We use chi square goodness of fit test to test whether the data come from a binomial distribution.

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