document.write( "Question 1120076: #6
\n" ); document.write( "You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 35 bacteria reveals a sample mean of ¯x=78 hours with a standard deviation of s=6.2\r
\n" ); document.write( "\n" ); document.write( " hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.45 hours at a 90% level of confidence.\r
\n" ); document.write( "\n" ); document.write( "What sample size should you gather to achieve a 0.45 hour margin of error? Round your answer up to the nearest whole number.\r
\n" ); document.write( "\n" ); document.write( "n = bacteria \n" ); document.write( "
Algebra.Com's Answer #735779 by Boreal(15235)\"\" \"About 
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Use a z first to get an idea and then look at the t-value
\n" ); document.write( "the margin of error is equal to t(df=unknown)*s/sqrt)(n) and that is equal to 0.45
\n" ); document.write( "Start with sample size of 100
\n" ); document.write( "t=1.66
\n" ); document.write( "1.66*6.2/sqrt(100)=1.029
\n" ); document.write( "let n=500
\n" ); document.write( "1.645*6.2/sqrt(n)=0.45
\n" ); document.write( "10.199=0.45 sqrt(n)
\n" ); document.write( "22.664=sqrt (n)
\n" ); document.write( "n=513.67 or 514\r
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