Question 1201383
population is assumed to be 95% vaccinated equals a population ratio of .95.
sample of 300 finds that 240 of them were fully vaccinated.
sample has a ratio of 240 / 300 = .8
standard error for the test is sqrt(.95 * .05 / 300) = .0125830574.
the population ratio is used in the calculation of the standard error for the test.
use the z-score formula to find the probability of getting a score less than .8.
z = (x - m) / s
z is the z-score
x is the sample ratio
m is the population ratio
s is the standard error.
you get z = (.8 - .9) / .0125830574 = -7.947194142.
the 99% confidence interval for the z-score would be plus or minus z = 2.575829303.
since the absolute value of the test z-score is greater than tha absolute value of the critical z-score, the test is considered significant and the conclusion is that ratio is not .95, but something less than that.