Question 510:
Asked on November 13, 2008
Tags:
Sample Size ,
Confidence Level
1
Answer:
No answer provided yet.
- For this question we need to find the sample size needed in order to meet the margin of error of +/- 5% using a 95% confidence level. The critical value associated with this level is 1.96, which we can look up using the percentile to z-score calculator. We're given an expected servicing rate of 30%, which we can use to build our standard deviation. The variance is .3*.7 = .21 and the square root of this is the standard deviation =SQRT(.21) = .458. Now we setup an equation to solve for the unknown sample size given our standard deviation and critical value of z.
- The margin of error is the standard error of the mean SEM * the critical z value of 1.96, so working backwards from a margin of .05, the SEM = .05/1.96= .0255.
- So the SEM is .0255 which is made up of the SD/ SQRT(n). Using the standard deviation we found of .458 and solving for the unknown sample size n we have the equation .458/sqrt(n) = .0255
- Squaring both sides = .21/n = .000651
- Isolating n gets us .000651n = .21 or n = .21/.000651 = 322.6
- Since we cannot ask part of a person, we round up to the nearest person to get 323.
- We can confirm our results using the confidence interval around a proportion calculator, the proportion was .3*323 = 97. Entering 97 and 323 gets us in-fact the desired margin of error of .05.
- So we'd need to sample 323 customers to have a margin of error of +/- 5%, which gives us a 95% confidence interval of between 25% and 35%.