Final answer:
The question involves determining if the current percentage of 18-25-year-olds who use marijuana or hashish is different from a historical percentage using a hypothesis test. A z-test is used to compare the sample proportion to the historical value, and the decision to reject or not reject the null hypothesis is based on whether the z-value falls within the critical value range for a significance level of α = 0.05.
Step-by-step explanation:
A recent poll of 2200 randomly selected 18-25-year-olds revealed that 255 currently use marijuana or hashish. To determine if the percentage of current users has changed from the historical percentage of 12.5% in 1997, a hypothesis test can be performed using the given significance level α = 0.05.
To perform the test, we calculate the test statistic z using the formula:
z = (p - P) / sqrt(P(1-P)/n)
Where:
- p is the sample proportion (255/2200)
- P is the historical proportion (0.125)
- n is the sample size (2200)
After calculating the sample proportion and plugging the values into the formula, we compare the calculated z-value with the critical z-values for a two-tailed test at the 0.05 significance level. If the calculated z-value falls outside the range of the critical z-values, we reject the null hypothesis and conclude that there is sufficient evidence to indicate a change in the percentage of 18-25-year-olds who currently use marijuana or hashish since 1997.