For each of the following situations, state whether you'd use a chi-square goodness-of-fit test, a chi-square test of homogeneity, a chi-square test of independence, or some other statistical test: a) A brokerage firm wants to see whether the type of account a customer has (Silver, Gold, or Platinum) affects the type of trade s that customer makes (in person, by phone, or on the Internet ). It collects a random sample of trades made for its customers over the past year and performs a test. b) That brokerage firm also wants to know if the type of account affects the size of the account (in dollars). It performs a test to see if the mean size of the account is the same for the three account types. c) The academic research office at a large community college wants to see whether the distribution of courses chosen (Humanities, Social Science, or Science) is different for its residential and nonresidential students. It assembles last semester's data and performs a test.
a) Because its a qualitative type,so the brokerage firm can use the chi square test for independency.
b) From the above constraints the brokerage firm can use chi square test because here also found variables are independent
c ) The brokerage firm can use chi square test to found the goodness of the distribution course for residential and non residential.
the expected value of the random variable : 0, 1 and 2