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 AGES 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 Degrees of Freedom for this hypothesis test is: Question 22 options: a) 10 b) 6 c) 8 d) 4 e) 12

Answer 1

The Degrees of Freedom (df) for the hypothesis test of age against opinion on marijuana legalization in a 4x3 contingency table is 6. In statistics, degrees of freedom define the shape of the t-distribution used in t-tests when calculating the p-value. Depending on the sample size, different degrees of freedom will display different t-distributions.

Step-by-step explanation:

A social researcher is testing the independence of two variables: individual's age and their opinion on the legalization of marijuana. A contingency table is provided with data collected from 1500 individuals. To determine the Degrees of Freedom (df) for this hypothesis test, we use the formula df = (r - 1) × (c - 1), where r is the number of rows and c is the number of columns in the table. Since the table has 4 rows (age groups) and 3 columns (opinions), the calculation is df = (4 - 1) × (3 - 1) = 3 × 2 = 6.

In this scenario, the correct answer from the given options is b) 6.

Degrees of freedom are the number of independent variables that can be estimated in a statistical analysis and tell you how many items can be randomly selected before constraints must be put in place.

Within a data set, some initial numbers can be chosen at random. However, if the data set must add up to a specific sum or mean, for example, the number in the data set is constrained to evaluate the values of all other values in a data set, then meet the set requirement.

Degrees of freedom are always the number of units within a given set minus 1. It is always minus one because, if parameters are placed on the data set, the last data item must be specific so all other points conform to that outcome.