Here is a hypothesis testing question I'm trying to work out but am struggling with how to draw a conclusion, maybe I'm not defining the null hypothesis correctly.
The question is as follows: Test the hypothesis that at least 68% of a population went to the movies once in the past year with a significance level of 5%. We surveyed 4000 people and found 3012 did go at least once in the past year.
Here I defined the null hypothesis as this: at least 68% (p >= .68) of the population went to the movies in the past year. (so the alternative hypothesis is that less than 68% of the population went)
Assuming the null hypothesis to be true, I calculated the standard deviation of the population to be 0.0074.
So, the Z-score = ((3012/4000)-0.68))/0.0074 = 9.86.
Here the critical z-value is 1.65 (for the 5% significance level).
Here is where I'm stuck -- what does this tell me? Is there something I'm doing wrong where identifying the null hypothesis?