document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=197815>Question 197815</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In order for applicants to work for the state department, they must take a test in the language of the country where they plan to work. The data below shows the relationship between the number of years that applicants have studied a particular language and the grades they received on the proficiency exam. \r<BR>\n" );
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document.write( "Applicant #1	2	3	4	5	6	7	8	9<BR>\n" );
document.write( "Years, x   4	5	5	6	4	7	3	8	4<BR>\n" );
document.write( "Grades, y  62	69	76	83	74	91	59	94	73\r<BR>\n" );
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document.write( "Part 1 (10 points0: Find the mean years for study for the 9 randomly selected applicants. Show the formula that you will use and then calculate the mean age.\r<BR>\n" );
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document.write( "Answer:  Formula: \r<BR>\n" );
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document.write( "              Mean:  \r<BR>\n" );
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document.write( "Using the r calculated, test the significance of the correlation coefficient using a = 0.01 and the claim k = 0. Design the test using the 7-steps hypothesis test.  \r<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "1.  H0 :  k = 0<BR>\n" );
document.write( "Ha : k <BR>\n" );
document.write( "2.  a = 0.01<BR>\n" );
document.write( "3.  Find the test statistic t.<BR>\n" );
document.write( "4.  Find the critical t0 <BR>\n" );
document.write( "5.  Define the rejection region. <BR>\n" );
document.write( "6.  State the statistical decision. <BR>\n" );
document.write( "7.  Application interpretation.\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 #148301 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=148301\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  In order for applicants to work for the state department, they must take a test in the language of the country where they plan to work. The data below shows the relationship between the number of years that applicants have studied a particular language and the grades they received on the proficiency exam. <BR>\n" );
document.write( "Applicant #1 2 3 4 5 6 7 8 9<BR>\n" );
document.write( "Years, x 4 5 5 6 4 7 3 8 4<BR>\n" );
document.write( "Grades, y 62 69 76 83 74 91 59 94 73 <BR>\n" );
document.write( "Part 1 (10 points0: Find the mean years for study for the 9 randomly selected applicants. Show the formula that you will use and then calculate the mean age. <BR>\n" );
document.write( "Answer: Formula:<BR>\n" );
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document.write( "Add the \"Years\" numbers and divide by 9 to get the following <BR>\n" );
document.write( "Mean: 5.1111...<BR>\n" );
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document.write( "Comment: the r value is 0.933675...<BR>\n" );
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document.write( "Using the r calculated, test the significance of the correlation coefficient using a = 0.01 and the claim k = 0. Design the test using the 7-steps hypothesis test. <BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "1. H0 : k = 0<BR>\n" );
document.write( "Ha : k is not 0<BR>\n" );
document.write( "2. a = 0.01<BR>\n" );
document.write( "3. Find the test statistic t.<BR>\n" );
document.write( "t = 0.933675/sqrt[(1-0.933675^2)/(9-2)] = 6.8977<BR>\n" );
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document.write( "4. Find the critical t0<BR>\n" );
document.write( "Critical values for a 2-tail test with alpha = 1% and df = 8 is t = 3.355<BR>\n" );
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document.write( "5. Define the rejection region.<BR>\n" );
document.write( "t-values that are less than -3.355 or greater than 3.355<BR>\n" );
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document.write( "6. State the statistical decision.<BR>\n" );
document.write( "Since the test statistic is in the reject interval, reject Ho.<BR>\n" );
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document.write( "7. Application interpretation.<BR>\n" );
document.write( "We reject the Ho claim that there is no linear correlation between<BR>\n" );
document.write( "years of study and grades.  The test results imply there is some <BR>\n" );
document.write( "linear correlation between those factors.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
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