Hi

You have to do a z-test given the sample size is above 30.

You first state the null hypothesis which states that the mean allowance = 3.65. You then stae the alternative hypothesis which states that mean allowance is not equal to 3.65. Hence, you will do a two-tailed or sided z-test.

The formula =

z = (M - X)/sd/sq(n)

M = Population mean = 3.65

X = Sample mean = 3.69

sd = Standard deviation = .24

sq(n) = square root of N

You will get a calculated z-value. You must see whether it falls within -1.96 to +1.96. If it does, you say that the means do not differ from each other. But if the value is outside this range, you say that means differs.