A second sample is to be drawn with the goal of producucing

A second sample is to be drawn with the goal of producucing a new 95% confidence interval for themean with a margin of error, E, no greater than $10. What is the minimum sample size, n, required to achieve this goal?

8.98 Because of inadequate public school budgets and lack of money available to teachers for class- room materials, many teachers often use their own money to buy materials used in the classrooms. A random sample of 100 public school teachers selected from an eastern state showed that they spent an average of $290 of their own money on such materials during the 2011-2012 school year. The pop- ulation standard deviation was $70.

Solution

Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.05% LOS is = 1.96 ( From Standard Normal Table )
Standard Deviation ( S.D) = 70
ME =10
n = ( 1.96*70/10) ^2
= (137.2/10 ) ^2
= 188.238 ~ 189