Research Sample Size

Sample size
The process of determining the proper sample size was established through a series of calculations and after obtaining all the possible sample sizes, the largest one was taken into consideration to collect the closest number to a representative sample of the population. The following two equations where used: Equation 1:
N=z2 *(p.q) E2
N= sample size
Z=level of confidence interval at 95% so z=1.96
P=estimated percent of population
E=acceptable sample error expressed as a percent (5%).

Equation 2:

N=s2*z2
E2
N= sample size
S=(minimum-maximum value) and divide the range by 6.
Z=level of confidence interval at 95% so z=1.96.
E=acceptable sample error expressed as a percent (5%).

For each question the series of calculations lead to the following results:
The sample size for question 1 is calculated using equation 1 and n=245.8624 rounded to n=246.
The sample size for question 2 is calculated using equation 1 and n=368.79 rounded to n=369.
The sample size for question 3 is calculated using equation 1 and n=288.12 rounded to n=289.
The sample size for question 4 is calculated using equation 1 and n=349.5856 rounded to n=350.
The sample size for question 5 is calculated using equation 1 and n=276.5952 rounded to n=277.
The sample size for question 6 is calculated using equation 1 and n=248.8624 rounded to n=246.
The sample size for question 7 is calculated using equation 1 and n=368.7936 rounded to n=369.
The sample size for question 8 is calculated using equation 1 and n=349.5856 rounded to n=350.
The sample size for question 9 is calculated using equation 1 and n=368.7936 rounded to n=369.
The sample size for question 10, 11, and 12 are calculated using equation 2 the following way:
N=4/62*1.962
0.52
N=sample size
S=(5-1)/6=4/6=
Z=95% equivalent to z=1.96
E=the average between two scales. Then 2-1=1/2=0.5
Therefor the sample size n=6.8295 rounded to n=7
The sample size for question 13 is calculated using