document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=129432>Question 129432</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Problem 1:<BR>\n" );
document.write( "Harold Hacker recently read in a national golf magazine that the average weekend golfer carries a handicap of 15 strokes and the standard deviation is 4 strokes. Harold manages a local men’s church league and just tallied the end-of-season totals. The 64 players in Harold’s league finished the year with an average handicap of 14 strokes.\r<BR>\n" );
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document.write( "a. Set up the null and alternative hypotheses to test if the average handicap in Harold’s league is not the same as the national average reported in the magazine.\r<BR>\n" );
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document.write( "b. Test your hypothesis using &#61537; = 0.02.\r<BR>\n" );
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document.write( "c. Find the p value.\r<BR>\n" );
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document.write( "d. Based on Harold’s end-of-season data, what can you conclude?<BR>\n" );
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document.write( "Problem 2:<BR>\n" );
document.write( "The players on last year’s football team at State College were able to bench press a mean of 312 lb. Coach Juarez made it clear to the players during spring training that the team’s average best lift had to improve. A special weight-training program was launched, and all the players participated. In an effort to measure the team’s progress, the coach recorded the heaviest lifts of the starting offensive and defensive lineups at the start of this season. Results are as follows:<BR>\n" );
document.write( "					346	412	332	285	396	461	321	275<BR>\n" );
document.write( "					246	315	298	347	430	419	406	311<BR>\n" );
document.write( "					319	385	377	365	385	400\r<BR>\n" );
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document.write( "a. State the appropriate null and alternative hypotheses.\r<BR>\n" );
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document.write( "b. Calculate the test statistic.<BR>\n" );
document.write( "HINT sample mean=356.43 lb<BR>\n" );
document.write( "Sample standard deviation = 56.05 lb\r<BR>\n" );
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document.write( "c. At &#61537; = 0.01, should Coach Juarez reject the null hypothesis?\r<BR>\n" );
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document.write( "d. Assuming the starting lineup is a representative sample, what conclusion can the coach draw?\r<BR>\n" );
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document.write( "Problem 3:<BR>\n" );
document.write( "a) Johnson’s Service Center has devised three potential options available to preferred customers who redeem coupons and buy at least 10 gallons of fuel when they stop in. Option A is a flat 3 cents off each gallon. Option B is a combination of 2 cents off plus another $1 discount on the regular price of a $5 deluxe car wash. Option C is a $2 discount on the same $5 deluxe car wash but no reduction in the fuel purchase. The owner, Harold Johnson, ran each option on three different two-week trial periods and tracked daily sales receipts from those customers who redeemed their coupons. Results are shown in the table below: <BR>\n" );
document.write( "Option A	Option B	Option C<BR>\n" );
document.write( "$453<BR>\n" );
document.write( "507<BR>\n" );
document.write( "513<BR>\n" );
document.write( "521<BR>\n" );
document.write( "511<BR>\n" );
document.write( "615<BR>\n" );
document.write( "601<BR>\n" );
document.write( "552<BR>\n" );
document.write( "551<BR>\n" );
document.write( "505<BR>\n" );
document.write( "515<BR>\n" );
document.write( "512<BR>\n" );
document.write( "476<BR>\n" );
document.write( "427	$492<BR>\n" );
document.write( "514<BR>\n" );
document.write( "536<BR>\n" );
document.write( "511<BR>\n" );
document.write( "528<BR>\n" );
document.write( "678<BR>\n" );
document.write( "611<BR>\n" );
document.write( "653<BR>\n" );
document.write( "596<BR>\n" );
document.write( "516<BR>\n" );
document.write( "534<BR>\n" );
document.write( "543<BR>\n" );
document.write( "498<BR>\n" );
document.write( "437	$467<BR>\n" );
document.write( "525<BR>\n" );
document.write( "516<BR>\n" );
document.write( "500<BR>\n" );
document.write( "435<BR>\n" );
document.write( "462<BR>\n" );
document.write( "411<BR>\n" );
document.write( "674<BR>\n" );
document.write( "512<BR>\n" );
document.write( "559<BR>\n" );
document.write( "624<BR>\n" );
document.write( "711<BR>\n" );
document.write( "512<BR>\n" );
document.write( "416<BR>\n" );
document.write( "	<BR>\n" );
document.write( "a) State the null hypothesis to test for equal population means.<BR>\n" );
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document.write( "b) Below are the results from EXCEL of ANOVA of the data at the 0.05 level of significance. Do the sample data indicate the at least one of the three population mean total returns is different from the others? Why? (Explain using “F” and “Fcrit” – a drawing is fine.)\r<BR>\n" );
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document.write( "Anova: Single Factor					<BR>\n" );
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document.write( "SUMMARY					<BR>\n" );
document.write( "Groups	Count	Sum	Average	Variance		<BR>\n" );
document.write( "Column 1	14	7259	518.5	2555.962		<BR>\n" );
document.write( "Column 2	14	7647	546.2143	4340.335		<BR>\n" );
document.write( "Column 3	14	7324	523.1429	8389.209		<BR>\n" );
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document.write( "ANOVA						<BR>\n" );
document.write( "Source of Variation	SS	df	MS	F	P-value	    F crit<BR>\n" );
document.write( "Between Groups	6169	2	3084.5	0.605377	0.550917    3.2381<BR>\n" );
document.write( "Within Groups	198711.6	39	5095.168			<BR>\n" );
document.write( "						<BR>\n" );
document.write( "Total	204880.6	41	 	 	 	 \r<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 #94644 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=94644\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Problem 1:<BR>\n" );
document.write( "Harold Hacker recently read in a national golf magazine that the average weekend golfer carries a handicap of 15 strokes and the standard deviation is 4 strokes. Harold manages a local men’s church league and just tallied the end-of-season totals. The 64 players in Harold’s league finished the year with an average handicap of 14 strokes. <BR>\n" );
document.write( "a. Set up the null and alternative hypotheses to test if the average handicap in Harold’s league is not the same as the national average reported in the magazine.<BR>\n" );
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document.write( "Ho: mu = 15<BR>\n" );
document.write( "Ha: mu is not 15<BR>\n" );
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document.write( "b. Test your hypothesis using &#61537; = 0.02.<BR>\n" );
document.write( "t(14) = (14-15)/[4/sqrt(64)] = -1*8/14 = -4/7 = -0.5714..<BR>\n" );
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document.write( "c. Find the p value. <BR>\n" );
document.write( "p-value = P(-10<t<-0.5714 with df = 63) = 0.2848...<BR>\n" );
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document.write( "d. Based on Harold’s end-of-season data, what can you conclude?<BR>\n" );
document.write( "The p-value is greater than 1% (half of 2% of this two-tailed test)<BR>\n" );
document.write( "so we Fail to reject Ho.<BR>\n" );
document.write( "Harold's results are statistically in keping with the published<BR>\n" );
document.write( "national average.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "StanH.<BR>\n" );
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