Answer:
37
Step-by-step explanation:
The first thing is to calculate critical z factor
the alpha and the critical z score for a confidence level of 90% is calculated as follows:
two sided alpha = (100% - 90%) / 200 = 0.05
critical z factor for two sided alpha of .05 is calculated as follows:
critical z factor = z factor for (1 - .05) = z factor for (.95) which through the attached graph becomes:
critical z factor = 2.58
Now we have the following formula:
ME = z * (sd / sqrt (N) ^ (1/2))
where ME is the margin of error and is equal to 6, sd is the standard deviation which is 14 and the value of z is 2.58
N the sample size and we want to know it, replacing:
6 = 2.58 * (14 / (N) ^ (1/2))
solving for N we have:
N = (2.58 * 14/6) ^ 2
N = 36.24
Which means that the sample size was 37.
