document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=362276>Question 362276</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 41)  The food marketing institute shows that 17% of households spend more than $100 per wee on groceries. Assume the population proportion is p=.17 and a simple random sample of 800 households will be selected from the population.   <BR>\n" );
document.write( "a)	Show the sampling distribution of p, the sample proportion of households spending more than $100 per week on groceries. <BR>\n" );
document.write( "b)	What is the probability that the sample proportion will be with in plus or minus .02 of the population proportion? <BR>\n" );
document.write( "c)	Answer part (b) for a sample of 1600. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #258157 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=258157\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The food marketing institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is p=.17 and a simple random sample of 800 households will be selected from the population.<BR>\n" );
document.write( "------- <BR>\n" );
document.write( "a) Show the sampling distribution of p, the sample proportion of households spending more than $100 per week on groceries.<BR>\n" );
document.write( "The mean of the sample means = 0.17<BR>\n" );
document.write( "The standard deviation of the sample means = sqrt[0.17*0.83/800]<BR>\n" );
document.write( "----------------------------------------------------- <BR>\n" );
document.write( "b) What is the probability that the sample proportion will be within plus or minus .02 of the population proportion?<BR>\n" );
document.write( "z(0.19) = (0.19-0.17)/sqrt(0.17*0.83/800] = 1.5060<BR>\n" );
document.write( "z(0.15) = -1.5060<BR>\n" );
document.write( "P(0.15< p < 0.19) = P(-1.5060< z <1.5060) = 0.8679<BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( " <BR>\n" );
document.write( "c) Answer part (b) for a sample of 1600.<BR>\n" );
document.write( "Put 1600 in place of 800 in the calculations.<BR>\n" );
document.write( "=============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );