document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1083817>Question 1083817</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A new piece of equipment is suspected of having faulty temperature control the desired temperature is  supposed to be 68 dergree and a random sample of 45 readings are  collected and the mean of these is 69.178 with a S.E of 0.483. at  the level significance 0.05  . what would your concluison have been around this hypothisis  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #697895 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=697895\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> desired temperature is 68 degrees.\r<BR>\n" );
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document.write( "sample size is 45<BR>\n" );
document.write( "mean of samples is 69.178<BR>\n" );
document.write( "standard error of sample is .483\r<BR>\n" );
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document.write( "z-score of sample = (69.178 - 68) / .483 = 2.44\r<BR>\n" );
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document.write( "since the faulty readings could be high or low, a two tailed distribution is assumed.\r<BR>\n" );
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document.write( "a significance level of .05 would be divided by 2 to get an alpha of .025 on each end.\r<BR>\n" );
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document.write( "an alpha of .025 on each end gives you a critical z-score of plus or minus 1.96.\r<BR>\n" );
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document.write( "the z-score of 2.44 is greater than the critical z-score, therefore the results of the test are statistically significant and you can conclude that the temperature readings are not within the prescribed limits.\r<BR>\n" );
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document.write( "notice that you were given the standard error, and not the standard deviation of the sample.\r<BR>\n" );
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document.write( "standard error is equal to standard deviation divided by square root of sample size.\r<BR>\n" );
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document.write( "using this formula, the standard deviation of your sample would have been based on this formula to get:\r<BR>\n" );
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document.write( "se = sd / sqrt(ss)\r<BR>\n" );
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document.write( "se is standard error<BR>\n" );
document.write( "sd is standard deviation<BR>\n" );
document.write( "ss is sample size\r<BR>\n" );
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document.write( ".483 = sd / sqrt(45)\r<BR>\n" );
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document.write( "solve for sd to get sd = .483 * sqrt(45) = 3.24.\r<BR>\n" );
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document.write( "in order for the readings not to be considered out of limits, a test with a sample of 45 should have given you readings between what is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/060502.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "you could calculate this using the z-score formula.\r<BR>\n" );
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document.write( "that formula is z = (x-m)/se\r<BR>\n" );
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document.write( "at 95% two tailed confidence interval, the critical z-score is 1.96.\r<BR>\n" );
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document.write( "to find the high side limits for 95% confidence interval, formula becomes:\r<BR>\n" );
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document.write( "1.96 = (x-68)/.483\r<BR>\n" );
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document.write( "solve for x to get x = 1.96 * .483 + 68 = 68.95\r<BR>\n" );
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document.write( "similar calculations using a z-score of -1.96 will get you the low side raw score limit.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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