Question 1077133
the assumed population proportion is .078 (7.8% / 100 = .078)


the sample proportion is 18/120 = .15.


pp is the population proportion
sp is the sample proportion


the sample size is 120.


n is the sample size.


the standard error of the sample is equal to sqrt(pp * pq / n) = sqrt(.078 * .922 / 120) = .024481 rounded to 6 dp.


sp is equal to the sample proportion.
pp is equal to the assumed population proportion
sq is = to 1 - sp
pq is equal to 1 - pp
n is the sample size.
dp = decimal places.


the test is to see if the proportion has increased, therefore the test is for a one tail distribution.


the alpha is .05.


the critical z-score is 1.645 rounded to 3 dp.


the z-score of the sample is equal to (.15 - .078) / .024481 = 2.941 rounded to 3 dp.


this is based on the general formula that z = (x-m)/s


z is the z-score
x is the sample mean proportion
m is the assumed population mean proportion
s is the standard error.


since the test z-score of 2.941 is much higher than the critical z-score of 1.645, you can reject the null hypothesis indicating that the percentage has, in fact, increased since then.


this involves hypothesis testing of a proportion.


a reference is shown below:


<a href = "https://onlinecourses.science.psu.edu/stat200/node/53" target = "_blank">https://onlinecourses.science.psu.edu/stat200/node/53</a>