Question

Are TV commercials louder than their surrounding programs? To find out, researchers collected data on $50$randomly selected commercials in a given week. With the television’s volume at a fixed setting, they measured the maximum loudness of each commercial and the maximum loudness in the first $30$seconds of regular programming that followed. Assuming conditions for inference are met, the most appropriate method for answering the question of interest is

(a) a one-proportion z test.

(b) a one-proportion z interval.

(c) a paired t test.

Short answer

The correct answer is (c) a paired$t-$test.

Step-by-step solution

Given Information

The maximum loudness in the first $30$ seconds of regular programming that followed.

Explanation

The question of interest involves the population mean the difference between the commercial and the regular programming.

The normal distribution is used for the population proportion and the Student t-distribution is used for the population mean, thus we will need to use the Student t-distribution.

It is best to use a test because we wish to test if there is a difference or not, and thus the correct answer is (c) a paired $t$-test.