Final answer:
To answer if the difference in the proportion of 40 to 59-year-old moviegoers is significant, a z-test for a proportion is performed, comparing the survey data to the stated 32% proportion and determining if the z-value is in the critical region at a 0.01 significance level.
Step-by-step explanation:
The question asks whether there is a statistically significant difference between the proportion of the 40- to 59-year-old age group observed in a theatre complex's survey and the stated proportion of the movie-going population. To determine this, a hypothesis test for a proportion can be performed using the z-test.
The null hypothesis (H0) assumes that the observed proportion (p) is equal to the stated proportion (p0), while the alternative hypothesis (H1) posits that the observed proportion is different from the stated proportion.
Given the observed number of moviegoers aged 40 to 59 is 170 out of 423, the sample proportion is 170/423.
The test statistic is calculated by comparing the sample proportion to the stated proportion of 0.32, adjusted for the standard error of the proportion. At the 0.01 level of significance, we would determine if the z-value falls within the critical region to either reject or fail to reject the null hypothesis.