Question

1. In a study on the likability of comedians, 10 participants observed one of two comedians (one who was humorous and one who was not humorous), and rated how likeable these comedians were on a 9-point scale from 1 (not likeable at all) to 9 (very likeable). The ratings are the data below. Test to see if the humorous comedian was liked more or less than the nonhumorous comedian, using alpha = .05 and four steps. Also calculate and interpret effect size and explained variance if appropriate.]

Answer 1

a. 84 < n + (n + 2) + (n + 4) < 96

b. 26 < n < 30

Explanation:

using 'n' to represent the smallest even number, the next even number would be 'n + 2' and the next even number would be 'n + 4'. so, the expression to represent three consecutive even numbers is: n + (n + 2) + (n + 4).

since the sum of the these numbers needs to be between 84 and 96, we can set up the following inequality:

84 < n + (n + 2) + (n + 4) < 96

in order to solve for 'n', we must first combine like terms:

84 < 3n + 6 < 96

subtract 6 from all sides: 84 - 6 < 3n + 6 - 6 < 96 - 6 or 78 < 3n < 90

divide 3 by all sides: 78/3 < 3n/3 < 90/3 or 26 < n < 30.