Posted by marie on Wednesday, August 26, 2009 at 7:27pm.
3 In 1999, a sample of 200 instore 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 pvalue. (d) Test whether normality may be assumed.

statistics  MathGuru, Wednesday, August 26, 2009 at 9:47pm
This problem fits a binomial proportion 2sample ztest using proportions.
Hypotheses:
Ho: p1 = p2
Ha: p1 < p2 >onetailed 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 1p.
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 pvalue or the actual level of this test statistic by using a ztable. 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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