document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=811546>Question 811546</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5.	The average salary of senior managers in the construction industry is $180,000 per year. Suppose we would like to take a sample of senior managers at a newly established company XYZ to see whether the mean annual salary is different from that of the industry. 								(5 marks)\r<BR>\n" );
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document.write( "This is a two tailed test, because what I want to calculate is whether it is equal to, or not equal to x amount. I would call the industry mean o1 and company XYZ o2.\r<BR>\n" );
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document.write( "a.	State the null and alternative hypotheses.\r<BR>\n" );
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document.write( "Null: Ho1 = Ho2: This states that the mean of one is the same as the second.<BR>\n" );
document.write( "Alternative: Ho1 &#8800; H02: This states that the mean of one is not the same as the second.\r<BR>\n" );
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document.write( "b.	Suppose a sample of 40 senior managers at XYZ showed a sample mean annual salary of $170,000. Assume a population standard deviation of $30,000. With  = .05 as the value of significance, what is your conclusion?\r<BR>\n" );
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document.write( "&#61656;	First, I calculate the test statistic by:<BR>\n" );
document.write( "&#61656;	Sample mean-population mean/ standard dev. x square root of sample<BR>\n" );
document.write( "&#61656;	So, it becomes 170,000-180,000/ 30,000 x 6.32<BR>\n" );
document.write( "&#61656;	I calculate this to be: -0.0527<BR>\n" );
document.write( "&#61656;	Because z< 0, this represents the area in the lower tail <BR>\n" );
document.write( "&#61656;	This means that the area below -0.0527 shows a probability of 0.4801<BR>\n" );
document.write( "&#61656;	Because it is a two tailed test, I would double this and calculate 0.9602. \r<BR>\n" );
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document.write( "Using the P-value approach, and the rule of (reject null is p < a), it says I should accept null which is incorrect as the means are obviously different.\r<BR>\n" );
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document.write( "&#61656;	The two tailed rejection rule is to reject null is z <-1.96 or z > 1.96<BR>\n" );
document.write( "ic <BR>\n" );
document.write( "Using the critical value approach, I can determine that my test statistic is less than 1.96, which is the zvalue for a/2.\r<BR>\n" );
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document.write( "Why is it right one way, and not the other? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #488801 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=488801\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The average salary of senior managers in the construction industry is $180,000 per year. Suppose we would like to take a sample of senior managers at a newly established company XYZ to see whether the mean annual salary is different from that of the industry. (5 marks) <BR>\n" );
document.write( "This is a two tailed test, because what I want to calculate is whether it is equal to, or not equal to 180,000.<BR>\n" );
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document.write( "a. State the null and alternative hypotheses. <BR>\n" );
document.write( "Null: x-bar = 180,000.<BR>\n" );
document.write( "Alternative: x-bar # 180,000<BR>\n" );
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document.write( "b. Suppose a sample of 40 senior managers at XYZ showed a sample mean annual salary of $170,000. Assume a population standard deviation of $30,000. With alpha = .05 as the value of significance, what is your conclusion?\r<BR>\n" );
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document.write( "z(170,000) = (170,000-180,000)/[30,000/sqrt(40)] = -2/3<BR>\n" );
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document.write( "p-value = 2*P(z < -2/3) = 2*normalcdf(-100,-2/3) = 0.5050<BR>\n" );
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document.write( "Conclusion:: Since the p-value is greater than 5%, fail<BR>\n" );
document.write( "to reject Ho.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( " \r<BR>\n" );
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document.write( " </SPAN>\n" );
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