document.write( "Question 1048816: If you could help me w/ this problem I would really appreciate it!\r
\n" ); document.write( "\n" ); document.write( "Why is a 99% confidence interval wider than a 95% confidence interval?\r
\n" ); document.write( "\n" ); document.write( "Thank you! \n" ); document.write( "

Algebra.Com's Answer #664392 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "For a $\"95\"$ % confidence interval, we will look up the $\"z\"$ values that separate the middle $\"95\"$ % of the area beneath the normal distribution from the remaining $\"5\"$ %. This remaining $\"5\"$ % is split between the right and left tails and half of $\"5\"$ % in each tail (i.e., $\"2.5\"$ % or $\".025\"$ ). The $\"z\"$ values that separate the middle $\"95\"$ % from the outer $\"5\"$ % are ą $\"1.960\"$ and our $\"z\"$ multiplier is $\"1.960\"$ .\r
\n" ); document.write( "\n" ); document.write( "What if we wanted to be more conservative and use a $\"99\"$ % confidence interval? Now we need the $\"z\"$ values that separate the middle $\"99\"$ % from the outer $\"1\"$ %. There will be $\"1\"$ % split between the left and right tails. The $\"z\"$ values that separate the middle $\"99\"$ % from the outer $\"1\"$ % are ą $\"2.58\"$ and our $\"z\"$ multiplier for a $\"99\"$ % confidence interval is $\"2.576\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The value of the $\"multiplier\"$ $\"+increases\"$ as the $\"confidence\"$ $\"+level\"$ $\"+increases\"$ . This leads to $\"wider\"$ intervals for higher confidence levels. We are more confident of catching the population value when we use a wider interval.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );