document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1081064>Question 1081064</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I've finished most of the questions already, but would like someone to check it they are correct. Thank you tutors for the help in advance!\r<BR>\n" );
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document.write( "We gather a sample of 100 people from a College and measure everyone’s age in the sample.  The average age is 26 with a sample standard deviation of 3 years.  \r<BR>\n" );
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document.write( "What is average of a student? <BR>\n" );
document.write( "ans:26<BR>\n" );
document.write( "Why does X &#773; vary randomly? <BR>\n" );
document.write( "ans: different ages/dates equals different results(?)<BR>\n" );
document.write( "What is our best guess of the distribution of X &#773;? <BR>\n" );
document.write( "ans: random(?)<BR>\n" );
document.write( "Construct a 90% C.I.? <BR>\n" );
document.write( "ans: 23.2, 28.8<BR>\n" );
document.write( "Is it plausible that µ is 27 years old?<BR>\n" );
document.write( "ans: yes\r<BR>\n" );
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document.write( "Test the hypothesis that u is greater than 27 years old a=.05?<BR>\n" );
document.write( "ii.Is the hypothesis considered one sided or two sided? <BR>\n" );
document.write( "one sided\r<BR>\n" );
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document.write( "iii.If the hypothesis is true, what is the distribution of X &#773; ?<BR>\n" );
document.write( "random\r<BR>\n" );
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document.write( "iv.Is the answer to part (iii) the same as 2c? <BR>\n" );
document.write( "yes\r<BR>\n" );
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document.write( "v.What is the value of the TTest?<BR>\n" );
document.write( ".025\r<BR>\n" );
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document.write( "vii.	What is TCritical?<BR>\n" );
document.write( "2\r<BR>\n" );
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document.write( "viii.Is the hypothesis likely or not likely to be true? <BR>\n" );
document.write( "true\r<BR>\n" );
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document.write( "ix.If your conclusion in part viii is wrong, what type of error did you make? <BR>\n" );
document.write( "type II\r<BR>\n" );
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document.write( "x.In this example, what is the probability of a type 1 error?<BR>\n" );
document.write( ".004\r<BR>\n" );
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document.write( "xi.Use the 68-96-99.7 rule to approximate the p-value.  What is the approximate p-value? <BR>\n" );
document.write( ".018\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #695155 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=695155\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What is average of a student? <BR>\n" );
document.write( "ans:26<BR>\n" );
document.write( "Why does X &#773; vary randomly? <BR>\n" );
document.write( "BECAUSE DIFFERENT SAMPLES WOULD HAVE DIFFERENT AVERAGES/MEANS<BR>\n" );
document.write( "What is our best guess of the distribution of X &#773;? <BR>\n" );
document.write( "THE BEST GUESS OF THE MEAN IS 26 AND THE BEST GUESS OF THE SD IS 3, BECAUSE THIS IS THE ONLY INFORMATION WE HAVE.<BR>\n" );
document.write( "Construct a 90% C.I.?  NOTE: 1-SIDED CONFIDENCE INTERVALS ARE MORE DIFFICULT, SO HERE I WILL USE A TWO-SIDED ONE<BR>\n" );
document.write( "ans: (25.5,  26.5)<BR>\n" );
document.write( "Is it plausible that µ is 27 years old?<BR>\n" );
document.write( "BECAUSE THE 90% CONFIDENCE INTERVAL FAILS TO CONTAIN THE VALUE 27, WE SAY THAT IT IS UNLIKELY TO BE 27.<BR>\n" );
document.write( "Test the hypothesis that u is greater than 27 years old a=.05?<BR>\n" );
document.write( "ii.Is the hypothesis considered one sided or two sided? <BR>\n" );
document.write( "one sided <BR>\n" );
document.write( "iii.If the hypothesis is true, what is the distribution of X &#773; ?<BR>\n" );
document.write( "Ho: MU < =27<BR>\n" );
document.write( "Ha: MU >27<BR>\n" );
document.write( "THE SAMPLING DISTRIBUTION IS MEAN 26 AND SD 0.3 THE SD COMES FROM s/sqrt(n)=3/10<BR>\n" );
document.write( "t(df=99,0.90). t >1.29 is critical value.<BR>\n" );
document.write( "t=(26-27)/0.3=-3.33.<BR>\n" );
document.write( " Fail to reject Ho.\r<BR>\n" );
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document.write( "iv.Is the answer to part (iii) the same as 2c? <BR>\n" );
document.write( "yes and no.  It is not likely to be 27 in both instances, and it is definitely not likely to be greater than 27 even with a one-way test<BR>\n" );
document.write( "v.What is the value of the TTest?<BR>\n" );
document.write( "IT IS (26-27)/0.3=-3.33<BR>\n" );
document.write( "vii.	What is Critical?t >1.29<BR>\n" );
document.write( "2 <BR>\n" );
document.write( "viii.Is the hypothesis likely or not likely to be true? <BR>\n" );
document.write( "THE NULL HYPOTHESIS IS LIKELY TO BE TRUE.  I WOULD HAVE PHRASED THE QUESTION REGARDING THE NULL HYPOTHESIS.  THE EXPERIMENTAL HYPOTHESIS IS NOT TRUE.<BR>\n" );
document.write( "ix.If your conclusion in part viii is wrong, what type of error did you make? <BR>\n" );
document.write( "TYPE II, BECAUSE IF WE ACCEPT A FALSE Ho, WE ARE MAKING AN ERROR OF THE SECOND TYPE.<BR>\n" );
document.write( "x.In this example, what is the probability of a type 1 error? ACTUALLY 0. THE PROBLEM HERE IS THAT THE SAMPLE MEAN IS 26 AND WE ARE HYPOTHESIZING THAT THE TRUE VALUE IS GREATER THAN 27 WITH A SAMPLE SIZE OF 100, AND THAT IS IMPOSSIBLE BECAUSE THE CONFIDENCE INTERVAL WILL ALWAYS CONTAIN A VALUE LESS THAN 27.  AM I MISREADING SOMETHING?\r<BR>\n" );
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document.write( "xi.Use the 68-96-99.7 rule to approximate the p-value. What is the approximate p-value? 1.\r<BR>\n" );
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