document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1156754>Question 1156754</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a program designed to help patients stop​ smoking, 156 patients were given sustained​ care, and 84.1​% of them were no longer smoking after one month. Use a 0.01 significance level to test the claim that 80​% of patients stop smoking when given sustained care. I have solved the test statistic and it is correct but I just need the p- value for the hypothesis test. Thanks in advance! \r<BR>\n" );
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document.write( "Upper H 0​: p equals 0.8<BR>\n" );
document.write( "Upper H 1​: p not equals 0.8<BR>\n" );
document.write( "The test statistic is 1.28.<BR>\n" );
document.write( "The p value for this hypothesis is ?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #779520 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=779520\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "z = (phat - p)/(sqrt(p*(1-p)/n))<BR>\n" );
document.write( "z = (0.841 - 0.8)/(sqrt(0.8*(1-0.8)/156))<BR>\n" );
document.write( "z = 1.28022458967168<BR>\n" );
document.write( "z = 1.28 is the test statistic<BR>\n" );
document.write( "Nice job on getting the correct test statistic\r<BR>\n" );
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document.write( "Now use a Z table found in the back of your stats textbook to find the area under the standard normal distribution.  <BR>\n" );
document.write( "If you do not have a book with you, then you can use a Z 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( "To find that<BR>\n" );
document.write( "P(Z < 1.28) = 0.89973<BR>\n" );
document.write( "note how I've highlighted the proper row and column which represent 1.20 and 0.08 combining to 1.28<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "P(Z > 1.28) = 1-P(Z < 1.28)<BR>\n" );
document.write( "P(Z > 1.28) = 1-0.89973<BR>\n" );
document.write( "P(Z > 1.28) = 0.10027 approximately\r<BR>\n" );
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document.write( "Due to the \"not equal\" sign in the alternative hypothesis, we have a two tailed test. This means we will double the result to get the area in both tails. \r<BR>\n" );
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document.write( "2*0.10027 = 0.20054\r<BR>\n" );
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document.write( "<font color=red size=4>The p value is approximately 0.20054</font>\r<BR>\n" );
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document.write( "Extra Info:<BR>\n" );
document.write( "At the significance level alpha = 0.01, we fail to reject the null. We can only reject the null if the p value is smaller than alpha. Failing to reject the null means we effectively \"accept\" the null hypothesis (until other data comes along to invalidate it). In other words, we conclude that p = 0.8 is the case. In the context of the problem, we conclude that 80% of patients quit smoking after one month.<BR>\n" );
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