document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187392>Question 1187392</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume that z is the test statistic. (Give your answers correct to two decimal places.)<BR>\n" );
document.write( "(a) Calculate the value of z for Ho: 𝜇 = 10, 𝜎 = 3.1, n = 41, x = 11.5. <BR>\n" );
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document.write( "Incorrect: Your answer is incorrect.<BR>\n" );
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document.write( "(b) Calculate the value of z for Ho: 𝜇 = 120, 𝜎 = 27, n = 30, x = 126.3. <BR>\n" );
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document.write( "(c) Calculate the value of z for Ho: 𝜇 = 18.2, 𝜎 = 3.7, n = 138, x = 18.89. <BR>\n" );
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document.write( "(d) Calculate the value of z for Ho: 𝜇 = 81, 𝜎 = 13.1, n = 53, x = 80.3. <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 #818418 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=818418\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assume that z is the test statistic. (Give your answers correct to two decimal places.)\r<BR>\n" );
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document.write( "(a) Calculate the value of z for Ho: 𝜇 = 10, 𝜎 = 3.1, n = 41, x = 11.5.\r<BR>\n" );
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document.write( "mean = m = 10<BR>\n" );
document.write( "standard deviation = sd = 3.1<BR>\n" );
document.write( "sample size = n = 41<BR>\n" );
document.write( "sample mean = x = 11.5\r<BR>\n" );
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document.write( "standard error = s = standard deviation divided by square root of sample size = 3.1 / sqrt(41) = .484139 rounded to 6 decimal places.\r<BR>\n" );
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document.write( "z = (x - m) / s = (11.5 - 10) / .484139 = 3.098283757.\r<BR>\n" );
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document.write( "round to two decimal places to get z = 3.1\r<BR>\n" );
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document.write( "(b) Calculate the value of z for Ho: 𝜇 = 120, 𝜎 = 27, n = 30, x = 126.3.\r<BR>\n" );
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document.write( "mean = m = 120<BR>\n" );
document.write( "standard deviation = sd = 27<BR>\n" );
document.write( "sample size = n = 30<BR>\n" );
document.write( "sample mean = x = 126.3\r<BR>\n" );
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document.write( "standard error = s = standard deviation divided by square root of sample size = 27 / sqrt(30) = 4.92950 rounded to 5 decimal places.\r<BR>\n" );
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document.write( "z = (x - m) / s = (126.3 - 120) / 4.92950 = 1.2167161984.\r<BR>\n" );
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document.write( "round to two decimal places to get z = 1.22.\r<BR>\n" );
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document.write( "(c) Calculate the value of z for Ho: 𝜇 = 18.2, 𝜎 = 3.7, n = 138, x = 18.89.\r<BR>\n" );
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document.write( "mean = m = 18.2<BR>\n" );
document.write( "standard deviation = sd = 3.7<BR>\n" );
document.write( "sample size = n = 138<BR>\n" );
document.write( "sample mean = x = 18.89\r<BR>\n" );
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document.write( "standard error = s = 3.7 / sqrt(138) = .314965 rounded to 6 decimal places.\r<BR>\n" );
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document.write( "z = (x - m) / s = (18.89 - 18.2) / .314965 = 2.190719602.\r<BR>\n" );
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document.write( "round to two decimal places to get z = 2.19.\r<BR>\n" );
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document.write( "(d) Calculate the value of z for Ho: 𝜇 = 81, 𝜎 = 13.1, n = 53, x = 80.3.\r<BR>\n" );
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document.write( "mean = m = 81<BR>\n" );
document.write( "standard deviation = sd = 13.1<BR>\n" );
document.write( "sample size = n = 53<BR>\n" );
document.write( "sample mean = x = 80.3\r<BR>\n" );
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document.write( "standard error = s = 13.1 / sqrt(53) = 1.799423 rounded to 6 decimal places.\r<BR>\n" );
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document.write( "z = (x - m) / s = (80.3 - 81) / 1.799423 = -.3890135894.\r<BR>\n" );
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document.write( "round to two decimal places to get z = -.39\r<BR>\n" );
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document.write( "here's a calculator that does all the dirty work for you.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.calculatorsoup.com/calculators/statistics/z-score-calculator.php\" target = \"_blank\">https://www.calculatorsoup.com/calculators/statistics/z-score-calculator.php</a>\r<BR>\n" );
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document.write( "i used this calculator on each of your problems.\r<BR>\n" );
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document.write( "your results are repeated below with the addition of the calculator results to show you that would get the same answer when using the calculator.\r<BR>\n" );
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document.write( "(a) Calculate the value of z for Ho: 𝜇 = 10, 𝜎 = 3.1, n = 41, x = 11.5.\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "mean = m = 10<BR>\n" );
document.write( "standard deviation = sd = 3.1<BR>\n" );
document.write( "sample size = n = 41<BR>\n" );
document.write( "sample mean = x = 11.5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "standard error = s = standard deviation divided by square root of sample size = 3.1 / sqrt(41) = .484139 rounded to 6 decimal places.\r<BR>\n" );
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document.write( "z = (x - m) / s = (11.5 - 10) / .484139 = 3.098283757.\r<BR>\n" );
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document.write( "\n" );
document.write( "round to two decimal places to get z = 3.1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/110801.jpg\" >\r<BR>\n" );
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document.write( "(b) Calculate the value of z for Ho: 𝜇 = 120, 𝜎 = 27, n = 30, x = 126.3.\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "mean = m = 120<BR>\n" );
document.write( "standard deviation = sd = 27<BR>\n" );
document.write( "sample size = n = 30<BR>\n" );
document.write( "sample mean = x = 126.3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "standard error = s = standard deviation divided by square root of sample size = 27 / sqrt(30) = 4.92950 rounded to 5 decimal places.\r<BR>\n" );
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document.write( "z = (x - m) / s = (126.3 - 120) / 4.92950 = 1.278020083\r<BR>\n" );
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document.write( "\n" );
document.write( "round to two decimal places to get z = 1.28.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/110802.jpg\" >\r<BR>\n" );
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document.write( "(c) Calculate the value of z for Ho: 𝜇 = 18.2, 𝜎 = 3.7, n = 138, x = 18.89.\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "mean = m = 18.2<BR>\n" );
document.write( "standard deviation = sd = 3.7<BR>\n" );
document.write( "sample size = n = 138<BR>\n" );
document.write( "sample mean = x = 18.89\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "standard error = s = 3.7 / sqrt(138) = .314965 rounded to 6 decimal places.\r<BR>\n" );
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document.write( "z = (x - m) / s = (18.89 - 18.2) / .314965 = 2.190719602.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "round to two decimal places to get z = 2.19.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/110803.jpg\" >\r<BR>\n" );
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document.write( "(d) Calculate the value of z for Ho: 𝜇 = 81, 𝜎 = 13.1, n = 53, x = 80.3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "mean = m = 81<BR>\n" );
document.write( "standard deviation = sd = 13.1<BR>\n" );
document.write( "sample size = n = 53<BR>\n" );
document.write( "sample mean = x = 80.3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "standard error = s = 13.1 / sqrt(53) = 1.799423 rounded to 6 decimal places.\r<BR>\n" );
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document.write( "z = (x - m) / s = (80.3 - 81) / 1.799423 = -.3890135894.\r<BR>\n" );
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document.write( "round to two decimal places to get z = -.39.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/110804.jpg\" >\r<BR>\n" );
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