SOLUTION: Determine the minimum sample size needed to construct a 95% confidence interval for the mean age of employees at a company. The estimate must be accurate to within 0.5 years. Assum

Question 1086421: Determine the minimum sample size needed to construct a 95% confidence interval for the mean age of employees at a company. The estimate must be accurate to within 0.5 years. Assume the sample standard deviation is 4.8 years. Your preliminary sample will be at least 30.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
95% CI width is t df=30, 0.975*4.8/sqrt(30)
=+/-2.045*4.8/sqrt(30)
=1.79
This is about 3.5 times higher than what is desired. Need to increase n 3.5 fold which means 12.25 fold before taking the square root.
Try a sample size of 375
+/-1.97*4.8/sqrt(375)=0.488
Since the only thing will change significantly is the sample size, want 1.97*4.8/sqrt (n)=0.5
0.5 sqrt (n)=1.97*4.8
sqrt(n)=18.912
n=357.66 or 358
This won't change the t-value significantly and the interval is 0.4997
n=357 gives an interval of 0.5004.
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