<p>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. A0 formulate appropriate hypotheses to test whether the percentage of debit card shoppers increased, B) carry out the test at alpha = .01. c) find the p value, d) test whether normality may be ussumed. determine if this is a right tail, a left tail, or a two tail test. Show the work and make a bell graph.</p><p>Let p1 and p2 be the percentage of debit card users in 1999 and 2004 respectively. Here we want to test whether the percentage of debit card shoppers increased. </p><p>That is we want to test the null hypothesis H0: p 1= p 2 against the alternative hypothesis</p><p>Ha : p1< p 2 .</p><p>Let p1 and p2 denote the sample proportion of debit card users in 1999 and 2004 based on a sample of size n1 and n2 respectively.</p><p>The test statistic for testing H0 is</p><p> p1- p 2 n p+ n p z= : N(0,1) , where p = 1 1 2 2 p(1- p )(1/ n1 + 1/ n 2 ) n1+ n 2</p><p>Here n1 = 200, n2 = 200, p1 = 42/200 = 0.21 and p2 = 62/200 = 0.31 200*0.21+ 200*0.31 42 + 62 104 Now p = = = = 0.26 200+ 200 400 400 0.21- 0.31 Thus the calculated value of z = = - 2.28 0.26*0.74*(1/ 200+ 1/ 200) The p-value of the test is given by, p-value = P[ Z < - 2.28] = 0.0113 Since the p-value is greater than 0.01, the level of significance, we accept the null hypothesis and conclude that the percentage of debit card shoppers is not increased.</p><p> d) Since n1 p1 = 200*0.21 = 42 >10 & n1 (1- p1 ) = 200*0.79 = 158 >10 and n2 p2 = 200*0.31 = 62 >10 & n2 (1- p2 ) = 200*0.69 = 138 >10, the normality assumption is satisfied.</p><p>Since the alternative hypothesis is Ha : p1< p 2 , the test is a left tailed test.</p>