document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=191043>Question 191043</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I started most of the work but I am not sure if I am doing it right. Please help.\r<BR>\n" );
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document.write( "Hypothesis Testing for Mean (Small Samples)\r<BR>\n" );
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document.write( "3. Metro Bank claims that the mean wait time for a teller during peak hours is less than 4 minutes. A random sample of 20 wait times has a mean of 2.6 minutes with a sample standard deviation of 2.1 minutes. <BR>\n" );
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document.write( "a. Use the critical value z0 method from the normal distribution to test for the population mean &#61549;. Test the company’s claim at the level of significance &#61537; = 0.05. \r<BR>\n" );
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document.write( "xbar = 2.6<BR>\n" );
document.write( "µ = 4<BR>\n" );
document.write( "s = 2.1<BR>\n" );
document.write( "n = 20\r<BR>\n" );
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document.write( "d.f = n – 1 = 20 – 1 = 19<BR>\n" );
document.write( "To find the critical value, use table 5 in Appendix B with d.f. = 19 and 0.05 in the “One Tail, &#61537;” column. Because the test is a left-tailed test, the critical value is negative. So<BR>\n" );
document.write( "t0 = -1.729\r<BR>\n" );
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document.write( "1.	H0 : u >= 4 minutes<BR>\n" );
document.write( "        Ha : u < 4 minutes<BR>\n" );
document.write( "2.	level of significance = 0.05<BR>\n" );
document.write( "3.	Test statistics: t = xbar -  µ / s/&#8730;n (2.6-4)/[2.1/sqrt(20)] = -2.9814<BR>\n" );
document.write( "4.	P-value or critical z0 or t0.    <BR>\n" );
document.write( "5.	Rejection Region: t < -1.729<BR>\n" );
document.write( "6.	Decision: Since -2.9814 is in the reject interval, Reject Ho.           <BR>\n" );
document.write( "7.	Interpretation: The mean time is not <= 4 minutes \r<BR>\n" );
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document.write( "b. Use the critical value z0 method from the normal distribution to test for the population mean&#61549;. Test the company’s claim at the level of significance &#61537; = 0.01.\r<BR>\n" );
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document.write( "xbar = 2.6<BR>\n" );
document.write( "µ = 4<BR>\n" );
document.write( "s = 2.1<BR>\n" );
document.write( "n = 20<BR>\n" );
document.write( "d.f = n – 1 = 20 – 1 = 19<BR>\n" );
document.write( "To find the critical value, use table 5 in Appendix B with d.f. = 19 and 0.01 in the “One Tail, level of significance ” column. Because the test is a left-tailed test, the critical value is negative. So<BR>\n" );
document.write( "t0 = 2.539\r<BR>\n" );
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document.write( "1.	H0 : u >= 4 minutes<BR>\n" );
document.write( "2.	Ha : u < 4 minutes <BR>\n" );
document.write( "3.	level of significance  = 0.01<BR>\n" );
document.write( "4.	Test statistics: <BR>\n" );
document.write( "5.	P-value or critical z0 or t0.  <BR>\n" );
document.write( "6.	Rejection Region:   <BR>\n" );
document.write( "7.	Decision:                                              <BR>\n" );
document.write( "8.	Interpretation:  \r<BR>\n" );
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document.write( "Hypothesis Testing for Proportions.\r<BR>\n" );
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document.write( "4. In a recent poll, it was found that 43% of registered U.S. voters would vote for the incumbent president. If 100 registered voters were sampled randomly, it was found that 35% would vote of the incumbent. Test the claim that the actual proportion is 43%. \r<BR>\n" );
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document.write( "1.	H0 : <BR>\n" );
document.write( "        Ha : <BR>\n" );
document.write( "2.	level of significance =<BR>\n" );
document.write( "3.	Test statistics: <BR>\n" );
document.write( "4.	P-value or critical z0 or t0.    <BR>\n" );
document.write( "5.	Rejection Region:  <BR>\n" );
document.write( "                                              <BR>\n" );
document.write( "6.	Decision:  <BR>\n" );
document.write( "7.	Interpretation: <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #143486 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=143486\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3. Metro Bank claims that the mean wait time for a teller during peak hours is less than 4 minutes. A random sample of 20 wait times has a mean of 2.6 minutes with a sample standard deviation of 2.1 minutes. \r<BR>\n" );
document.write( "\n" );
document.write( "a. Use the critical value z0 method from the normal distribution to test for the population mean &#61549;. Test the company’s claim at the level of significance &#61537; = 0.05. <BR>\n" );
document.write( "xbar = 2.6<BR>\n" );
document.write( "µ = 4<BR>\n" );
document.write( "s = 2.1<BR>\n" );
document.write( "n = 20 <BR>\n" );
document.write( "d.f = n – 1 = 20 – 1 = 19<BR>\n" );
document.write( "To find the critical value, use table 5 in Appendix B with d.f. = 19 and 0.05 in the “One Tail, &#61537;” column. Because the test is a left-tailed test, the critical value is negative. So<BR>\n" );
document.write( "t0 = -1.729 \r<BR>\n" );
document.write( "\n" );
document.write( "1. H0 : u >= 4 minutes<BR>\n" );
document.write( "Ha : u < 4 minutes<BR>\n" );
document.write( "2. level of significance = 0.05<BR>\n" );
document.write( "3. Test statistics: t = xbar - µ / s/&#8730;n (2.6-4)/[2.1/sqrt(20)] = -2.9814<BR>\n" );
document.write( "4. P-value or critical z0 or t0. <BR>\n" );
document.write( "5. Rejection Region: t < -1.729<BR>\n" );
document.write( "6. Decision: Since -2.9814 is in the reject interval, Reject Ho. <BR>\n" );
document.write( "7. Interpretation: The mean time is not <= 4 minutes <BR>\n" );
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document.write( "part \"a\" looks good<BR>\n" );
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document.write( "b. Use the critical value z0 method from the normal distribution to test for the population mean&#61549;. Test the company’s claim at the level of significance &#61537; = 0.01. <BR>\n" );
document.write( "xbar = 2.6<BR>\n" );
document.write( "µ = 4<BR>\n" );
document.write( "s = 2.1<BR>\n" );
document.write( "n = 20<BR>\n" );
document.write( "d.f = n – 1 = 20 – 1 = 19<BR>\n" );
document.write( "To find the critical value, use table 5 in Appendix B with d.f. = 19 and 0.01 in the “One Tail, level of significance ” column. Because the test is a left-tailed test, the critical value is negative. So<BR>\n" );
document.write( "t0 = 2.539 \r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "1. H0 : u >= 4 minutes<BR>\n" );
document.write( "2. Ha : u < 4 minutes <BR>\n" );
document.write( "3. level of significance = 0.01<BR>\n" );
document.write( "4. Test statistics: <BR>\n" );
document.write( "5. P-value or critical z0 or t0. <BR>\n" );
document.write( "6. Rejection Region: <BR>\n" );
document.write( "7. Decision: <BR>\n" );
document.write( "8. Interpretation: <BR>\n" );
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document.write( "Hypothesis Testing for Proportions. <BR>\n" );
document.write( "4. In a recent poll, it was found that 43% of registered U.S. voters would vote for the incumbent president. If 100 registered voters were sampled randomly, it was found that 35% would vote of the incumbent. Test the claim that the actual proportion is 43%. <BR>\n" );
document.write( "1. H0 : p = 0.43 <BR>\n" );
document.write( "Ha : p is not 0.43<BR>\n" );
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document.write( "2. level of significance =  alpha = 5%,<BR>\n" );
document.write( "3. Test statistics: z(0.35) = (0.35-0.43)*sqrt[0.43*0.57/100] = -1.6159<BR>\n" );
document.write( "4. P-value or critical z0 or t0.l: 2P(z<-1.6159) = 0.10611 <BR>\n" );
document.write( "5. Rejection Region: z<1.96 or z>1.96\r<BR>\n" );
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document.write( "6. Decision: Since the p-value is greater than 5%, Fail to reject Ho.<BR>\n" );
document.write( "7. Interpretation: The test does not provide evidence that <BR>\n" );
document.write( "lead to rejecting the poll results.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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