Question

A social researcher decides to test whether an individual's age and their opinion on the legalization of marijuana are independent. The researcher randomly interviews 1500 individuals to determine their opinion regarding the legalization of marijuana. The results are given in the following contingency table. OPINION ON THE LEGALIZATION OF MARIJUANA Individual's Age FOR AGAINST UNDECIDED Row Totals 17 - 27 a) 170 b) 100 c) 130 400 28 - 38 d) 155 e) 70 f) 125 350 39 - 49 g) 130 h) 100 i) 120 350 50 & Over j) 145 k) 130 l) 125 400 Column Totals 600 400 500 1500 The alternative hypothesis for this test is: Question 20 options: a) none of these b) The Two Population Classifications: Opinion on the legalization of marijuana and the person's age are dependent. c) The Two Population Classifications: Opinion on the legalization of marijuana and the person's age are a positive relationship. d) The Two Population Classifications: Opinion on the legalization of marijuana and the person's age are a negative relationship. e) The Two Population Classifications: Opinion on the legalization of marijuana and the person's age are independent.

Answer 1

The correct alternative hypothesis for the test is that the opinion on the legalization of marijuana and the person's age are dependent, indicating a possible relationship between these two variables.

Step-by-step explanation:

The student has asked how to formulate an alternative hypothesis for testing whether an individual's age and their opinion on the legalization of marijuana are independent. Based on the given contingency table and the possible options, the correct alternative hypothesis is: Opinion on the legalization of marijuana and the person's age are dependent. This hypothesis suggests that there is a relationship between the age of individuals and their opinions on the legalization of marijuana, which contradicts the null hypothesis that would state there is no relationship (the two variables are independent).

The alternative hypothesis is a statement that contradicts the null hypothesis and is used to determine if there is a significant difference between two variables. It is often written as an inequality to show that there is a difference between the two variables being tested.

For example, if we are testing whether a new drug is more effective than a placebo, the alternative hypothesis would be written as "the new drug is more effective than the placebo," or in inequality form, "the effectiveness of the new drug > the effectiveness of the placebo."