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 two-sample t test for a difference in means.

b. a two-sample t interval for a difference in means.

c. a paired t test for a mean difference.

d. a paired t interval for a mean difference.

e. a two-sample z test for a difference in proportions.

Short answer

Option(e) A two-sample z test for a difference in proportions is the most appropriate method for this question.

Step-by-step solution

Given information

We need to find most appropriate method for answering the question.

Simplify

In general, we know that there is a one-sample z test for each proportion.
However, there is a two-sample z test for two proportions.
Similarly, there is one sample t test for one mean and two sample t tests or intervals or paired t tests or intervals for two means.

For checking a difference, equality, increase, or reduction, use a test.
To estimate an interval in which the true value lies, use an interval.
Therefore, a two-sample z test for a difference in proportions in this query because we need to estimate the difference between the two proportions.
As a result, option (e) is the proper choice.