document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202069>Question 1202069</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Achaiah made a claim that at least 5% of the college male students drives racing car. His friend Sofia finds this hard to believe and decided to check the validity of Achaiah's claim, so she took a random sample. At 0.05, does Sofia have sufficient evidence to reject Achaiah's claim if there were 19 racing car in her sample of 750 cars? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #836690 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=836690\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "p = population proportion\r<BR>\n" );
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document.write( "n = sample size<BR>\n" );
document.write( "phat = sample proportion<BR>\n" );
document.write( "The job of phat is to estimate p.\r<BR>\n" );
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document.write( "In this problem we have<BR>\n" );
document.write( "n = 750<BR>\n" );
document.write( "phat = 19/750 = 0.025333 (approximate)<BR>\n" );
document.write( "alpha = 0.05 = significance level\r<BR>\n" );
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document.write( "Now let's set up the two hypotheses<BR>\n" );
document.write( "Null: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+%3E=+0.05 ALIGN=MIDDLE  ALT=\"p+%3E=+0.05\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Alternate: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+%3C+0.05 ALIGN=MIDDLE  ALT=\"p+%3C+0.05\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The claim \"at least 5% of the college male students drive a racing car\" is in the null. <BR>\n" );
document.write( "Technically the null should be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+0.05 ALIGN=MIDDLE  ALT=\"p+=+0.05\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but I'll go with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+%3E=+0.05 ALIGN=MIDDLE  ALT=\"p+%3E=+0.05\"   DISABLED_style= \"max-width:90%; height:auto;\" > to match up with the phrasing from the claim.<BR>\n" );
document.write( "The \"less than\" sign in the alternate hypothesis means we have a left tailed test.\r<BR>\n" );
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document.write( "The phat distribution will be centered at p = 0.05 and have standard error (SE) of...<BR>\n" );
document.write( "SE = sqrt(p*(1-p)/n)<BR>\n" );
document.write( "SE = sqrt(0.05*(1-0.05)/750)<BR>\n" );
document.write( "SE = 0.0079582 which is approximate\r<BR>\n" );
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document.write( "Calculate the z score for the phat value of phat = 0.025333<BR>\n" );
document.write( "z = (phat - p)/SE<BR>\n" );
document.write( "z = (0.025333 - 0.05)/0.0079582<BR>\n" );
document.write( "z = -3.09957<BR>\n" );
document.write( "z = -3.10\r<BR>\n" );
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document.write( "Now use a table such as this one<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.ztable.net/\">https://www.ztable.net/</a><BR>\n" );
document.write( "Similar tables are found in the back of your stats textbook.<BR>\n" );
document.write( "Alternatively you could use a stats calculator like this one<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://davidmlane.com/normal.html\">https://davidmlane.com/normal.html</a><BR>\n" );
document.write( "but I'll stick to the table route.\r<BR>\n" );
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document.write( "Use that table to see that<BR>\n" );
document.write( "P(Z < -3.10) = 0.00097<BR>\n" );
document.write( "This is the approximate area under the Z curve to the left of z = -3.10<BR>\n" );
document.write( "Recall we're doing a left tailed test, so this area represents the p-value.\r<BR>\n" );
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document.write( "p-value = 0.00097<BR>\n" );
document.write( "alpha = 0.05\r<BR>\n" );
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document.write( "The p-value is smaller than alpha, so we reject the null.<BR>\n" );
document.write( "We conclude the alternate hypothesis <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+%3C+0.05 ALIGN=MIDDLE  ALT=\"p+%3C+0.05\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be the case.\r<BR>\n" );
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document.write( "Answer: Sofia has sufficient evidence to reject Achaiah's claim<BR>\n" );
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