document.write( "Question 312937: 1. By measuring the amount of time it takes a component of a product to move from one workstation to the next, an engineer has estimated that the standard deviation is 1.8 seconds.
\n" ); document.write( "(a)How many measurements should be made in order t be 99% certain that the maximum error of estimation will not exceed 0.5 seconds?
\n" ); document.write( "(b) What sample size is required for a maximum error of 1 second?
\n" ); document.write( "2. In testing the hypothesis H0: u _>35 and Ha: u <35 using the p-value approach, a p - value of 0.0721 was obtained. If standard deviation = 8.1 find a sample mean which produced this p - value given that the sample of size n = 32 was randomly selected.
\n" ); document.write( "3.A study was conducted t estimated the mean amount spent on birthday gifts for a typical family having two children. A sample of 125 was taken, and the mean amount spent was $230. Assuming a standard deviation equal to $45 find the 95% confidence interval for u the mean for all such families. \n" ); document.write( "
Algebra.Com's Answer #223772 by stanbon(75887)\"\" \"About 
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1. By measuring the amount of time it takes a component of a product to move from one workstation to the next, an engineer has estimated that the standard deviation is 1.8 seconds.
\n" ); document.write( "(a)How many measurements should be made in order to be 99% certain that the maximum error of estimation will not exceed 0.5 seconds?
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\n" ); document.write( "n = [z*s/E]^2
\n" ); document.write( "n = [2.5758*1.8/0.5]^2 = 86 when rounded up
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\n" ); document.write( "(b) What sample size is required for a maximum error of 1 second?
\n" ); document.write( "Comment: Same procedure but use \"1\" in place of 0.5
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\n" ); document.write( "2. In testing the hypothesis H0: u >= 35 and Ha: u <35 using the p-value approach, a p-value of 0.0721 was obtained. If standard deviation = 8.1 find a sample mean which produced this p-value given that the sample of size n = 32 was randomly selected.
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\n" ); document.write( "Find the t-value with a left tail of 0.0721 when df = 31 : t = -1.4982
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\n" ); document.write( "Find the sample mean:
\n" ); document.write( "(x-bar-35)/[8.1/sqrt(31)] = -1.4982
\n" ); document.write( "x-bar-35 = -2.1796
\n" ); document.write( "---
\n" ); document.write( "x-bar = 32.8204
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\n" ); document.write( "\n" ); document.write( "3.A study was conducted to estimate the mean amount spent on birthday gifts for a typical family having two children. A sample of 125 was taken, and the mean amount spent was $230. Assuming a standard deviation equal to $45 find the 95% confidence interval for u the mean for all such families.
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\n" ); document.write( "sample mean: 230
\n" ); document.write( "E = (invT(0.975,124)*45/sqrt(125)) = 7.9664
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\n" ); document.write( "95% CI:
\n" ); document.write( "230-7.9664 < u < 230+7.9664
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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