document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=335182>Question 335182</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Hello I need help with my statistic homework I can't understand how this formula works  its random sample. the problem is <BR>\n" );
document.write( " a random sample of 600 high school boys showed 40 had taken diet pills during the past 30 days to lose weight the proportion of all high school boys who taken the diet pills to lose weight  H0 p=0.10 Ha;p#0.10<BR>\n" );
document.write( "1. state the null hypotheseis (H0) and the alternative hypothesesis (Ha)<BR>\n" );
document.write( "2. verify necessary data conditions for a z statistic and calculate the z statistic<BR>\n" );
document.write( "3. assuming the null hypothesis is true finf the p value ?<BR>\n" );
document.write( "4.are the results statistically significant at a significance level of a=0.05 ?what is the conclusion to the context? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #240289 by </B><A HREF=/tutors/aboutme.mpl?userid=jrfrunner><B>jrfrunner(365)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jrfrunner><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=jrfrunner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=240289\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. state the null hypotheseis (H0) and the alternative hypothesesis (Ha)<BR>\n" );
document.write( "--<BR>\n" );
document.write( "H0: P=0.10<BR>\n" );
document.write( "Ha: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%3C%3E0.10 ALIGN=MIDDLE  ALT=\"P%3C%3E0.10\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "note that this is a two tail test.<BR>\n" );
document.write( "P is the population proportion which is unknown<BR>\n" );
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document.write( "2. Technically, this is a binomial distribution problem, two outcomes for every student.  Very cumbersome to continue via binomial distribution!<BR>\n" );
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document.write( "if you can meet the requirement <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2AP%5B0%5D%3E10 ALIGN=MIDDLE  ALT=\"n%2AP%5B0%5D%3E10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2A%281-P%5B0%5D%29%3E10 ALIGN=MIDDLE  ALT=\"n%2A%281-P%5B0%5D%29%3E10\"   DISABLED_style= \"max-width:90%; height:auto;\" > then you can use the Normal approximation to the Binomial\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2AP%5B0%5D=600%2A%280.10%29=60 ALIGN=MIDDLE  ALT=\"n%2AP%5B0%5D=600%2A%280.10%29=60\"   DISABLED_style= \"max-width:90%; height:auto;\" >>10 and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2A%281-P%5B0%5D%29=600%2A%280.90%29=540 ALIGN=MIDDLE  ALT=\"n%2A%281-P%5B0%5D%29=600%2A%280.90%29=540\"   DISABLED_style= \"max-width:90%; height:auto;\" >>10, The requirement is met for Normal approximation<BR>\n" );
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document.write( "Find the critical value <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=type+I_error%3A+alpha=0.05 ALIGN=MIDDLE  ALT=\"type+I_error%3A+alpha=0.05\"   DISABLED_style= \"max-width:90%; height:auto;\" >, -/+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%280.05%2F2%29 ALIGN=MIDDLE  ALT=\"z%280.05%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=-/+z(0.025)=-/+1.96  (being two tail test the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha ALIGN=MIDDLE  ALT=\"alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" > has to be divided by half)<BR>\n" );
document.write( "--<BR>\n" );
document.write( "State the decision rule. <BR>\n" );
document.write( "If Z test statistic < -critical value=-1.96  or Z test statistic > critical value=1.96 then reject Ho<BR>\n" );
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document.write( "Compute the value of the Z test statistic. <BR>\n" );
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document.write( "phat=sample proportion=40/600=0.067<BR>\n" );
document.write( "test statistic: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z+=+%28phat-P%5B0%5D%29%2Fsqrt%28P%5B0%5D%2A%281-P%5B0%5D%29%2Fn%29 ALIGN=MIDDLE  ALT=\"Z+=+%28phat-P%5B0%5D%29%2Fsqrt%28P%5B0%5D%2A%281-P%5B0%5D%29%2Fn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B0%5D ALIGN=MIDDLE  ALT=\"P%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >=proportion under the null.<BR>\n" );
document.write( "Z= (0.067-0.10)/sqrt(0.10*(1-0.10)/600) =-2.69<BR>\n" );
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document.write( "Find the p-value<BR>\n" );
document.write( "P(Z<=-2.69)+P(Z>=2.69) =0.0036+0.0036=0.0072<BR>\n" );
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document.write( "Two ways to make the decision:<BR>\n" );
document.write( "1: compare the test statistic vs critical value as stated above<BR>\n" );
document.write( "test statistic Z=-2.69 < -critical value=-1.96, thus test falls in the reject region<BR>\n" );
document.write( "or<BR>\n" );
document.write( "compare the pvalue against the significance level, alpha<BR>\n" );
document.write( "since pvalue=0.0072 < <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha=0.05 ALIGN=MIDDLE  ALT=\"alpha=0.05\"   DISABLED_style= \"max-width:90%; height:auto;\" > then reject Ho<BR>\n" );
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document.write( "conclusion <BR>\n" );
document.write( "The proportion of students at this high school taking diet pills is not 10%<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );