Question

#462. Teacher Salaries Based on the 2017-2018 Average Starting Teacher Salaries by State measured by NEA, the average starting salary for teachers in Pennsylvania is $44,647, the sample size is 6,241 and the standard deviation is $759.00 If we want to get a 80% confidence interval with a small margin of error, say only 19. How many people do you need to sample? (Since a fraction of a person does not make sense, make sure to give the next largest whole number as your answer.) symbolic expression

Answer 1

Solution :

Given that,

standard deviation =  $\sigma$ = 759.00

Margin of error = E = 19

At 80% confidence level the z is ,

Z_$\alpha$/2 = Z_0.1 = 1.282

sample size = n = [Z_$\alpha$/2* $\sigma$ / E] ²

n = ( 1.282* 759 / 19 )²

n =2622.722852

Sample size = n =2623