document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=974214>Question 974214</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Pew Research Center conducted a survey of 1007 adults and found that 856 of them know what Twitter is.\r<BR>\n" );
document.write( "\n" );
document.write( "a.What is the point estimate for the number of adults who know what Twitter is?\r<BR>\n" );
document.write( "\n" );
document.write( "b.Use a 0.01 level of significance to test the claim that more than 75% of adults know what Twitter is.\r<BR>\n" );
document.write( "\n" );
document.write( "State the null and alternative hypotheses:\r<BR>\n" );
document.write( "\n" );
document.write( "Calculate the test statistic:\r<BR>\n" );
document.write( "\n" );
document.write( "Fine the p-value:\r<BR>\n" );
document.write( "\n" );
document.write( "Decision:\r<BR>\n" );
document.write( "\n" );
document.write( "Conclusion:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #596211 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=596211\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Given:<BR>\n" );
document.write( "x = 856<BR>\n" );
document.write( "n = 1007\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "p-hat = x/n<BR>\n" );
document.write( "p-hat = 856/1007<BR>\n" );
document.write( "p-hat = 0.85004965243297\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The point estimate is approximately <font color=\"red\">0.85004965243297</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(b)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Given:<BR>\n" );
document.write( "x = 856<BR>\n" );
document.write( "n = 1007<BR>\n" );
document.write( "p = 0.75<BR>\n" );
document.write( "phat = 0.85004965243297 (found in part a)<BR>\n" );
document.write( "alpha = 0.01\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hypothesis:<BR>\n" );
document.write( "H0: p = 0.75<BR>\n" );
document.write( "H1: p > 0.75 (claim)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Standard Error:<BR>\n" );
document.write( "SE = sqrt(p*(1-p)/n)<BR>\n" );
document.write( "SE = sqrt(0.75*(1-0.75)/1007)<BR>\n" );
document.write( "SE = 0.0136453883651\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Test Statisic:<BR>\n" );
document.write( "z = (phat - p)/SE<BR>\n" );
document.write( "z = (0.85004965243297 - 0.75)/0.0136453883651<BR>\n" );
document.write( "z = 7.3321220148531\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "p-value<BR>\n" );
document.write( "normalcdf(7.3321220148531, 99999) = 1.14 * 10^(-13)<BR>\n" );
document.write( "The p-value is so very small that it's effectively 0.<BR>\n" );
document.write( "No matter what the significance level is, we have statistically significant evidence to reject H0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Decision: Reject the null hypothesis\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Conclusion: There is enough significant evidence to conclude that the population proportion who are familiar with twitter is over 75%\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "------------------------------------------------------------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you need more one-on-one help, email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help\">jim_thompson5910@hotmail.com</a>. You can ask me a few more questions for free, but afterwards, I would charge you ($2 a problem to have steps shown or $1 a problem for answer only).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Alternatively, please consider visiting my website: <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">http://www.freewebs.com/jimthompson5910/home.html</a> and making a donation. Any amount is greatly appreciated as it helps me a lot. This donation is to support free tutoring. Thank you.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Jim\r<BR>\n" );
document.write( "\n" );
document.write( "------------------------------------------------------------------------------------------------------------------------ </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );