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3. The state office claims that the average income of people playing the lottery is at least 3 7,000. Assume that the income is normally distributed with a standard deviation of 5,? 56. Suppose that for a sample of25 households, it is found that the average income was 3 6,2 43 . [4 marks] a. What are the appropriate null and alternative hypotheses? b. What is the test statistic for this test? c. Give an estimate ofthep-value