document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183829>Question 1183829</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question 3<BR>\n" );
document.write( "Many people believe that the average number of Facebook friends is 338. The population standard deviation is 43.2. A random sample of 50 high school students in a country revealed that the average number of Facebook friends was 350. At α = 0.05,\r<BR>\n" );
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document.write( "a. Why was the sample collected?\r<BR>\n" );
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document.write( "b. Calculate the significant level for this hypothesis test.\r<BR>\n" );
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document.write( "c. Find the critical value for this test at α = 0.05.\r<BR>\n" );
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document.write( "d. Calculate the test value.\r<BR>\n" );
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document.write( "e. Based on the test value and the critical value is there enough evidence to conclude that the mean number of friends is greater than 338?\r<BR>\n" );
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document.write( "f. Determine whether it is a one  -  tail or a two - tail test.\r<BR>\n" );
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document.write( "g. Find the maximum error E for estimating population mean. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814427 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=814427\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a. The sample was collected to determine whether the belief that the average number of Facebook friends of 338 is still true.\r<BR>\n" );
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document.write( "b. The signicance level is <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;\" >, no need to calculate.  (But do you know what this value means?)\r<BR>\n" );
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document.write( "c.  By the CLT, the sampling distribution of the sample means is approximately normally distributed with mean <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu+=+338 ALIGN=MIDDLE  ALT=\"mu+=+338\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and standard dev <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma%2Fsqrt%28n%29+=+43.2%2Fsqrt%2850%29 ALIGN=MIDDLE  ALT=\"sigma%2Fsqrt%28n%29+=+43.2%2Fsqrt%2850%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "===> critical value for a ONE-TAILED test (will explain later why)  is 1.645.\r<BR>\n" );
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document.write( "d.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%28%28X-bar%29+-+mu%29%2F%28sigma%2Fsqrt%28n%29%29+=++%28350+-+338%29%2F%2843.2%2Fsqrt%2850%29%29+=+1.964 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "e.  By comparing the test value with the critical z, we reject the null hypothesis, and conclude that <BR>\n" );
document.write( "there is evidence that the average number of Facebook friends may have increased from 338.\r<BR>\n" );
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document.write( "f.  It is a one-tailed test because the sample value of 350 is quite far from 338 (on the high side), enough to suspect that the <BR>\n" );
document.write( "true sample mean may have increased from 338.\r<BR>\n" );
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document.write( "g.  Maximum error is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5B0.95%5D%2A%28sigma%2Fsqrt%28n%29%29+=+1.645%2A%2843.2%2Fsqrt%2850%29%29+=++10.05 ALIGN=MIDDLE  ALT=\"z%5B0.95%5D%2A%28sigma%2Fsqrt%28n%29%29+=+1.645%2A%2843.2%2Fsqrt%2850%29%29+=++10.05\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Done. </SPAN>\n" );
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