document.write( "Question 1166620: A researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 30 bacteria reveals a sample mean of
\n" ); document.write( "¯
\n" ); document.write( "x
\n" ); document.write( "=
\n" ); document.write( "64
\n" ); document.write( " hours with a standard deviation of
\n" ); document.write( "s
\n" ); document.write( "=
\n" ); document.write( "5.8
\n" ); document.write( " hours. He would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.8 hours at a 98% level of confidence.\r
\n" ); document.write( "\n" ); document.write( "What sample size should you gather to achieve a 0.8 hour margin of error?\r
\n" ); document.write( "\n" ); document.write( "He would need to sample
\n" ); document.write( " bacteria. \n" ); document.write( "

Algebra.Com's Answer #791287 by Boreal(15235) $\"\"$ $\"About$

You can put this solution on YOUR website!
start with z0.99 since we aren't sure yet of df for t
\n" ); document.write( "that is 2.326
\n" ); document.write( "the half-interval is 0.8 and is equal to z*s/sqrt(n) for the first approximation
\n" ); document.write( "0.8=2.326*5.8/sqrt(n)
\n" ); document.write( "0.8sqrt*n=2.326*5.8
\n" ); document.write( "square both sides
\n" ); document.write( "0.64n=182.00
\n" ); document.write( "n=284.375 or 285
\n" ); document.write( "At this point the t-value is a few more df than 285. From the calculator, n=288 or df=287 gives the desired margin of error, and that is the answer.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );