document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1076812>Question 1076812</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Need help with the t and p value on this one, thank you!<BR>\n" );
document.write( "Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.66. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows.<BR>\n" );
document.write( "4.9	4.2	4.5	4.1	4.4	4.3<BR>\n" );
document.write( "(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)<BR>\n" );
document.write( "x	=	 <BR>\n" );
document.write( "4.40<BR>\n" );
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document.write( "Correct: Your answer is correct.<BR>\n" );
document.write( "s	=	 <BR>\n" );
document.write( ".28<BR>\n" );
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document.write( "Correct: Your answer is correct.\r<BR>\n" );
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document.write( "(ii) Do the given data indicate that the population mean RBC count for this patient is lower than 4.66? Use &#945; = 0.10.<BR>\n" );
document.write( "(a) What is the level of significance? <BR>\n" );
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document.write( "0.10<BR>\n" );
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document.write( "Correct: Your answer is correct.<BR>\n" );
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document.write( "State the null and alternate hypotheses.<BR>\n" );
document.write( "H0: &#956; > 4.66; H1: &#956; = 4.66<BR>\n" );
document.write( "H0: &#956; = 4.66; H1: &#956; > 4.66    <BR>\n" );
document.write( "H0: &#956; = 4.66; H1: &#956; &#8800; 4.66<BR>\n" );
document.write( "H0: &#956; = 4.66; H1: &#956; < 4.66<BR>\n" );
document.write( "H0: &#956; < 4.66; H1: &#956; = 4.66<BR>\n" );
document.write( "Correct: Your answer is correct.\r<BR>\n" );
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document.write( "(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.<BR>\n" );
document.write( "The standard normal, since we assume that x has a normal distribution and &#963; is known.<BR>\n" );
document.write( "The Student's t, since we assume that x has a normal distribution and &#963; is unknown.    <BR>\n" );
document.write( "The Student's t, since we assume that x has a normal distribution and &#963; is known.<BR>\n" );
document.write( "The standard normal, since we assume that x has a normal distribution and &#963; is unknown.<BR>\n" );
document.write( "Correct: Your answer is correct.\r<BR>\n" );
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document.write( "What is the value of the sample test statistic? (Round your answer to three decimal places.) <BR>\n" );
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document.write( "-2.394<BR>\n" );
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document.write( "Incorrect: Your answer is incorrect.<BR>\n" );
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document.write( "(c) Find the P-value. (Round your answer to four decimal places.) <BR>\n" );
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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 #691428 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=691428\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Calculating the t test statistic\r<BR>\n" );
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document.write( "t = (xbar - mu)/(s/sqrt(n))<BR>\n" );
document.write( "t = (4.40-4.66)/(0.28/sqrt(6))<BR>\n" );
document.write( "t = -2.27452618972722<BR>\n" );
document.write( "t = -2.275\r<BR>\n" );
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document.write( "The t test statistic is approximately -2.275\r<BR>\n" );
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document.write( "Calculating the p value\r<BR>\n" );
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document.write( "We have two basic options to calculate the p value: a) using a table or b) using a calculator\r<BR>\n" );
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document.write( "Since your teacher wants it accurate to 4 decimal places, we'll have to use a calculator to get the desired accuracy. Using a TI calculator, you would type in  <font color=blue>tcdf(-99,-2.275,5)</font> as shown below<BR>\n" );
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document.write( "Note: Hit the 2ND key up at the top corner, then hit the VARS key. Scroll down to \"tcdf\" which is option number 6. The first two numbers \"-99, -2.275\" are the left and right bounds of the interval. Effectively this is the same as saying \"everything to the left of -2.275. The last value 5 is the degrees of freedom (df = n-1 = 6-1 = 5)\r<BR>\n" );
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document.write( "Doing all that, we get the p value of roughly 0.0359934669 which rounds to 0.0360 when you round to four decimal places. \r<BR>\n" );
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document.write( "Side Note: if you don't have a TI calculator, then you can use online calculators, such as <a  rel=nofollow HREF= \"http://stattrek.com/online-calculator/t-distribution.aspx\">this one</a>, to calculate the p value. </SPAN>\n" );
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