document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=370409>Question 370409</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hi, i need help with this. any kind of help will be appriciated. \r<BR>\n" );
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document.write( "Question : By statistics, faculty with rank of assistant professor (AP) finishing their 2nd year of employment at a higher education institution in Ontario earn an average of $ 68,500 per year with a standard deviation of $3500. In an attempt to verify this salary level, a random sample of 50 AP with 2 years of experiment was selected from a personnel database for all higher education institutions in Ontario.\r<BR>\n" );
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document.write( "a. Describe the sampling distribution of the sample mean ¯X of the average salary of these 50 AP.\r<BR>\n" );
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document.write( "b. Within what limit would you expect the sample mean to fall with probability .95\r<BR>\n" );
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document.write( "c. Calculate the probability that ¯X is greater than 70,000.\r<BR>\n" );
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document.write( "d. If the random sample actually produced a sample mean of 70,000, would you considerthis rather unusual? What conclusion might you draw then?\r<BR>\n" );
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document.write( "Thanks in advance. <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 #264253 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=264253\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Question : By statistics, faculty with rank of assistant professor (AP) finishing their 2nd year of employment at a higher education institution in Ontario earn an average of $ 68,500 per year with a standard deviation of $3500. In an attempt to verify this salary level, a random sample of 50 AP with 2 years of experiment was selected from a personnel database for all higher education institutions in Ontario.<BR>\n" );
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document.write( "a. Describe the sampling distribution of the sample mean ¯X of the average salary of these 50 AP.<BR>\n" );
document.write( "Ans: The mean of the sample means = 68,500<BR>\n" );
document.write( "The std of the sample means = 3500/sqrt(50)<BR>\n" );
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document.write( "b. Within what limit would you expect the sample mean to fall with probability .95<BR>\n" );
document.write( "Lower limit: x-bar = 68500-1.96* [3500/sqrt(50)] = 67529.85 <BR>\n" );
document.write( "Upper limit: x-bar = 68500+1.96* [3500/sqrt(50)] = 69470.15<BR>\n" );
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document.write( "c. Calculate the probability that ¯X is greater than 70,000.<BR>\n" );
document.write( "Find the t-value of 70,000<BR>\n" );
document.write( "I get t = 3.0305<BR>\n" );
document.write( "Find the probability that t is greater than that t-value when df = 49<BR>\n" );
document.write( "I get 0.0019<BR>\n" );
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document.write( "d. If the random sample actually produced a sample mean of 70,000, would you considerthis rather unusual?<BR>\n" );
document.write( "Ans: Rather unusual since 70,000 is more than 3 std's above the mean.<BR>\n" );
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document.write( "What conclusion might you draw then?<BR>\n" );
document.write( "Ans: The population mean is probably wrong.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
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