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Chapter 9: Problem 4

Electricity prices According to the U.S. Energy Information Administration, the average monthly household electricity bill in 2014 was \(\$ 114\) before taxes and fees. A consumer association plans to investigate if the average amount has changed this year. Define the population parameter of interest and state the null and alternative hypotheses for this investigation.

Short Answer

Expert verified
\( H_0: \mu = 114 \), \( H_a: \mu \neq 114 \)

Step by step solution

01

Step 1

Identify the population parameter of interest. In this case, we are looking at the average monthly household electricity bill.
02

Step 2

Define the population parameter. Let \( \mu \) represent the average monthly household electricity bill for the current year.
03

Step 3

State the null hypothesis. The null hypothesis \( H_0 \) is that the average monthly household electricity bill has not changed since 2014, so \( H_0: \mu = 114 \).
04

Step 4

State the alternative hypothesis. The alternative hypothesis \( H_a \) is that the average monthly household electricity bill has changed, so \( H_a: \mu eq 114 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Population Parameter
When conducting hypothesis testing, it is crucial to identify the population parameter you are interested in. A population parameter is essentially a numerical value that captures certain characteristics of a population. In the context of our exercise about electricity prices, the population parameter is the average monthly household electricity bill for this year.

The symbol commonly used for a population parameter related to an average is \( \mu \). In this case, \( \mu \) represents the average monthly household electricity bill for the current year. Understanding this allows us to frame what exactly we are testing, providing a baseline to compare our hypothesized estimates against the known value from previous years.
Null Hypothesis
The null hypothesis is a fundamental part of hypothesis testing and acts as the default or original claim. It presumes that there is no change or effect until proven otherwise. In hypothesis testing, we set up the null hypothesis to test if any observed effects in the data are due to chance.

For the problem of evaluating changes in electricity bills, the null hypothesis is stated as \( H_0: \mu = 114 \), which indicates that the average monthly bill for this year is the same as it was in 2014. The null hypothesis is what you aim to test against, and initially, is presumed true until there is significant evidence to suggest otherwise.
Alternative Hypothesis
The alternative hypothesis is what you consider if the null hypothesis is rejected. It suggests that there is a different outcome or effect than originally assumed.

In our exercise, the alternative hypothesis is explained as \( H_a: \mu eq 114 \). This suggests that the average monthly household electricity bill has indeed changed from the 2014 figure of $114. Unlike the null hypothesis which assumes no change, the alternative hypothesis opens the possibility of change solely as a result of the evidence provided by the data. It represents the researcher's initial suspicion or what they are trying to prove.

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Most popular questions from this chapter

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