Final answer:
The statistics instructor at EVC found that about 13.1 percent of a sample of students attended a Harry Potter midnight showing, less than the 20 percent hypothesized. A hypothesis test can be employed to determine if this result is statistically significant at the 1 percent level, leading to a potential conclusion that fewer than 20 percent of EVC students attended the showing.
Step-by-step explanation:
The topic under discussion is statistical analysis, specifically hypothesis testing. When the statistics instructor at Evergreen Valley College (EVC) wanted to test the belief that fewer than 20 percent of students attended the midnight showing of the latest Harry Potter movie, she conducted a survey of 84 students and found that 11 attended. This represents approximately 13.1 percent (11 out of 84), which is indeed less than 20 percent.
To determine if this sample proportion can be generalized to the population of EVC students, a hypothesis test can be conducted. The null hypothesis (H0) would state that the percentage of EVC students who attended the midnight showing is at least 20 percent, while the alternative hypothesis (H1) would claim that it is less than 20 percent.
Given a 1 percent level of significance, we would reject the null hypothesis if the test statistic falls into the critical region that corresponds to the most extreme 1 percent of the distribution assuming the null hypothesis is true. If the calculated test statistic indeed falls in this region, or the p-value is less than the level of significance (0.01), then we conclude there is sufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is less than 20 percent.