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3 In 1999, a sample of 200 in-store shoppers showed that 42 paid by debit card. In 2004, a sample
of the same size showed that 62 paid by debit card. (a) Formulate appropriate hypotheses to test
whether the percentage of debit card shoppers increased. (b) Carry out the test at รก = .01. (c) Find
the p-value. (d) Test whether normality may be assumed.

  • statistics -

    This problem fits a binomial proportion 2-sample z-test using proportions.

    Hypotheses:
    Ho: p1 = p2
    Ha: p1 < p2 -->one-tailed test (shows a specific direction)

    The formula is:
    z = (p1 - p2)/√[pq(1/n1 + 1/n2)]
    ...where 'n' = sample sizes, 'p' is (x1 + x2)/(n1 + n2), and 'q' is 1-p.

    I'll get you started:
    p = (42 + 62)/(200 + 200) = ? -->once you have the fraction, convert to a decimal (decimals are easier to use in the formula)
    q = 1 - p
    p1 = 42/200
    p2 = 62/200
    Convert all fractions to decimals. Plug those decimal values into the formula and find z. Once you have this value, you will be able to determine the p-value or the actual level of this test statistic by using a z-table. Determine the outcome of the test (whether or not to reject the null). Draw your conclusions from there.

    I hope this will help get you started.

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