SOLUTION: Please help! Thanks! In 2006, a sample of 200 in-store shoppers showed that 42 paid by debit card. In 2009, a sample of the same size showed that 80 paid by debit card. (a) Form

Question 1179111: Please help! Thanks!
In 2006, a sample of 200 in-store shoppers showed that 42 paid by debit card. In 2009, a sample of the same size showed that 80 paid by debit card. (a) Formulate appropriate hypotheses to test whether the percentage of debit card shoppers increased. (b) Carry out the test at alpha=0.01. (c) Find the pvalue. (d) Test whether normality may be assumed.
a. State the null and alternative hypotheses (you MUST label which is H0 and which is H1)
b. What is the critical value?
c. What is the test statistic?
d. Do you reject or fail to reject?
e. What is the pvalue?
f. Explain why normality can be assumed.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
this is a 2-sample proportion test, testing parameters π1, the true proportion in 2006, and π2, the true proportion in 2009.
p*, the combined proportion, is 122/400 or 0.305
np1 and n(1-p1) and np2 and n(1-p2) are all > 10, so may use normality.
p1=0.21 with n=200
p2=0.40 with n=200
Ho:π1 > = π2
Ha: π1 < π2
alpha is 0.01 p{reject Ho|Ho true}
critical value is z < -2.326 (the z for 0.0100)
test stat is z=-0.19/sqrt(0.305*0.695)(1/100)). sqrt(p hat-(1-p hat)/ ((1/n1)+(1/n2)))
=-0.19/0.046
=-4.13
Strongly reject Ho, p-value 0.00002.
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