document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203708>Question 1203708</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could adding a dash of pizzazz, like the promise of free pizza, turn our questionnaires<BR>\n" );
document.write( "into must-respond treasures? In our zany experiment, we mailed out 100 straightforward questionnaires with no extra perks and got 65 responses. Then, we sent 98<BR>\n" );
document.write( "questionnaires offering the tantalizing reward of a free pizza, and we received 78 replies.<BR>\n" );
document.write( "Does this intriguing data suggest that adding incentives like free pizza might be the key<BR>\n" );
document.write( "to turning our questionnaires into real page-turners (i.e., the proportion of responses<BR>\n" );
document.write( "are more when offered free pizza)? Use α = 0.05 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839526 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=839526\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you want to test whether adding a dish of pizzazz gets more replies or whether the sample differences are due to random variations in different samples.\r<BR>\n" );
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document.write( "no pizzazz gets 65 out of 100 responses.<BR>\n" );
document.write( "pizzazz gets 78 out of 98 responses.\r<BR>\n" );
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document.write( "p1 = 65/100 = .65.<BR>\n" );
document.write( "p2 = 78/98 = .7959183673.<BR>\n" );
document.write( "p0 = (65 + 78) / (100 + 98) = 143/198 = .7222222222.<BR>\n" );
document.write( "1 - p0 = .2777777777.\r<BR>\n" );
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document.write( "z-score formula is:<BR>\n" );
document.write( "z = (p1 - p2) / s<BR>\n" );
document.write( "s = standard error.\r<BR>\n" );
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document.write( "s = sqrt(p0 * (1-p0) * (1/n1 + 1/n2))<BR>\n" );
document.write( "n1 is sample size of sample 1.<BR>\n" );
document.write( "n2 is sample size of sample 2.<BR>\n" );
document.write( "s becomes equal to sqrt(.7222222222 * .2777777777 * (1/100 + 1/98)) = .0636654379.\r<BR>\n" );
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document.write( "z = (p1 - p2) / s becomes z = (.65 - .7959183673) / .0636654379 which is equal to -2.291955764.\r<BR>\n" );
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document.write( "the area to the left of that z-score of -2.291955764 is equal to .0109540673.<BR>\n" );
document.write( "that's your test alpha.<BR>\n" );
document.write( "it is less than your critical alpha of .05.<BR>\n" );
document.write( "that makes the results of the test significant, which means that the sample results are most likely not due to random variations in sample proportions, but an actual difference.<BR>\n" );
document.write( "the conclusion is that the use of pizzazz does generate greater response rates.\r<BR>\n" );
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document.write( "i used an online calculator and got the same results.<BR>\n" );
document.write( "here they are:\r<BR>\n" );
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document.write( " </SPAN>\n" );
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