There are 4 branches of a local bank. Last year, branches A, B, C and D handled 27%, 23%, 20% and 30% of all transactions, respectively. A new shopping mall has recently opened, and the vice president of the bank wants to see if this opening has produced any changes in the distribution of transactions. The transactions for a week, selected at random after the opening of the new mall, are: Branch A B C D Total Transactions 683 648 427 732 2490 Test, at α = 0.01, whether the distribution of transactions has changed after the opening of the new mall. (a) Write down the null and alternative hypotheses. (b) Check the necessary conditions for carrying out the hypothesis testing. (c) Give the rejection region. Find the observed test statistic. Give the decision and final conclusion.
There are 4 branches of a local bank. Last year, branches A, B, C and D handled 27%,
23%, 20% and 30% of all transactions, respectively. A new shopping mall has recently
opened, and the vice president of the bank wants to see if this opening has produced
any changes in the distribution of transactions. The transactions for a week, selected at
random after the opening of the new mall, are:
Branch A B C D Total
Transactions 683 648 427 732 2490
Test, at α = 0.01, whether the distribution of transactions has changed after the opening
of the new mall.
(a) Write down the null and alternative hypotheses.
(b) Check the necessary conditions for carrying out the hypothesis testing.
(c) Give the rejection region. Find the observed test statistic.
Give the decision and final conclusion.
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