Homework help needed (math)?

3.  

for the standard error (for the mean) to be within 2 points standard error  =   Z_critical*population standard deviation/ sqrt(N)  2 =   Z_critical* 4.8/sqrt(N)    

for 90 % confidence range which goes from 

5 % to  95%   

P(z< Z_critical) =  0.95  

so if you reverse look-up to two closest value in a z-table , you get

P(z< 1.64) = .94950 

P(z< 1.65) = 0.95053

since it is almost exactly in the middle 

Z_critical = 1.645  is usually used  

2 = 1.645*4.8/sqrt(N) 

2*sqrt(N) = 1.645*4.8 

sqrt(N) = 1.645*4.8/2  

square both sides 

N = (1.645*4.8/2)^2 = 15.586704

since N must be an integer    

N = 16  

4.  

If only have one point of data for an estimate of the mean 

point estimate of mean =  $23.45 

Z_critical( for 90% confidence is same as in 3) =  1.645  

N =  49 

standard deviation = 2.80 

so just plug in the number into the formulas 

CI_Low = mean -  Z_critical* standard deviation/sqrt(N) 

CI_Low=  23.45 -  1.645*2.80/sqrt(49) = 23.45  -1.645*0.40=  22.792

CI_high = mean  -Z_critical*standard deviation/sqrt(N) 

since it's the same number 

CI_High = 23.45 + 1.645*2.80/sqrt(49) =  24.108 

range (22.792  ,  24.108)       

so if you have to round to the penny to 

include  

(22.79,  24.11)