document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196688>Question 1196688</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ou want to rent an unfurnished one-bedroom apartment in Boston next year. The mean monthly rent for a simple random sample of 32 apartments advertised in the local newspaper is $1 400. Assume that the standard deviation is known to be $220.\r<BR>\n" );
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document.write( "Find a 99% confidence interval for the mean monthly rent for unfurnished one-bedroom apartments available for rent in this community. </SPAN>\n" );
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document.write( "At 99% confidence, the z critical value is roughly z = 2.576<BR>\n" );
document.write( "Use a table like this<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf\">https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf</a><BR>\n" );
document.write( "to get that value. Look at the bottom row labeled \"Z\" and above the 99% confidence level.\r<BR>\n" );
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document.write( "We use a Z distribution instead of a T distribution since <BR>\n" );
document.write( "a) sigma is given<BR>\n" );
document.write( "b) n > 30\r<BR>\n" );
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document.write( "Given info:<BR>\n" );
document.write( "n = 32 = sample size<BR>\n" );
document.write( "xbar = 1400 = sample mean<BR>\n" );
document.write( "sigma = 220 = population standard deviation\r<BR>\n" );
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document.write( "Side note: We often won't know what sigma is since it's a population parameter. The goal of statistics is to estimate parameter. Use the sample standard deviation (variable 's') to estimate sigma, if sigma is unknown.\r<BR>\n" );
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document.write( "E = margin of error<BR>\n" );
document.write( "E = z*sigma/sqrt(n)<BR>\n" );
document.write( "E = 2.576*220/sqrt(32)<BR>\n" );
document.write( "E = 100.18288875851\r<BR>\n" );
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document.write( "L = lower boundary of confidence interval<BR>\n" );
document.write( "L = xbar - E<BR>\n" );
document.write( "L = 1400 - 100.18288875851<BR>\n" );
document.write( "L = 1299.8171112415<BR>\n" );
document.write( "L = 1299.82\r<BR>\n" );
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document.write( "U = upper boundary of confidence interval<BR>\n" );
document.write( "U = xbar + E<BR>\n" );
document.write( "U = 1400 + 100.18288875851<BR>\n" );
document.write( "U = 1500.1828887585<BR>\n" );
document.write( "U = 1500.18\r<BR>\n" );
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document.write( "Answer: <font color=red>(1299.82, 1500.18)</font> which is in the format (L, U)<BR>\n" );
document.write( "This is equivalent to saying 1299.82 < mu < 1500.18 in the format L < mu < U.<BR>\n" );
document.write( "Your answers may slightly vary depending on how you round the decimal values.<BR>\n" );
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