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Chapter 4: Problem 32

Indicate whether the analysis involves a statistical test. If it does involve a statistical test, state the population parameter(s) of interest and the null and alternative hypotheses. Utilizing the census of a community, which includes information about all residents of the community, to determine if there is evidence for the claim that the percentage of people in the community living in a mobile home is greater than \(10 \%\).

Short Answer

Expert verified
This analysis does involve a statistical test, and the population parameter of interest is the proportion of residents in the community who live in a mobile home. The null hypothesis is that the proportion is \(10 \%\), and the alternative hypothesis is that the proportion is greater than \(10 \%\).

Step by step solution

01

Identify if the case involves a statistical test

In this case, the task is to determine if there is evidence to support a claim. This involves making a decision about a population parameter based on sample data. Therefore, this involves a statistical test.
02

Identify the population parameter of interest

The population parameter of interest in this problem is the proportion of residents in the community who live in a mobile home.
03

Establish the null and alternative hypotheses

In hypothesis testing, the null hypothesis is typically a statement of 'no effect' or 'no difference'. In this case, the null hypothesis would be that the population proportion of residents living in mobile homes is \(10 \%\). The alternative hypothesis is the one we want to provide evidence for, which in this case is that the proportion is greater than \(10 \%\). So: \nNull hypothesis (\(H_0\)): The population proportion (\(p\)) of residents living in a mobile home is \(10 \%\). \nAlternative hypothesis (\(H_1\) or \(H_a\)): The population proportion (\(p\)) of residents living in a mobile home is greater than \(10 \%\).

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Key Concepts

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

Statistical Test
Understanding whether an analysis involves conducting a statistical test is crucial for hypothesis testing. A statistical test is used to make a decision about a population parameter based on sample data. In the context of the provided exercise, the goal is to determine if there is evidence to support the claim that more than 10% of the community's residents live in mobile homes. Given that we are making a decision about a population proportion based on collected data, a statistical test is indeed involved here. This type of test will help to infer if the observed data significantly deviates from what is expected under the null hypothesis.
Population Parameter
The term population parameter refers to a numerical characteristic of a population. For instance, it could be the mean or proportion of a certain trait within the entire population. In our exercise, the population parameter of interest is the proportion of residents living in mobile homes within the community. The proportion, often represented by the symbol \(p\), is an essential aspect of the statistical test. It's the value we are attempting to estimate and make inferences about based on our sample data.
Null Hypothesis
In statistical hypothesis testing, the null hypothesis is a default statement that there is no effect or no significant difference. It is usually a statement of equality, such as 'equal to,' 'less than or equal to,' or 'greater than or equal to.' It is not a claim of absolute truth, but rather a position that there isn't enough evidence to accept an alternative claim. For the community census example, the null hypothesis (\(H_0\)) is that the population proportion (\(p\)) of residents living in mobile homes is exactly 10% (\(p = 0.10\)).
Alternative Hypothesis
Contrary to the null hypothesis, the alternative hypothesis is what the researcher wants to provide evidence for. This hypothesis suggests that there is an effect or difference, and it is typically expressed as inequality. In our specific example, the alternative hypothesis (often denoted as \(H_1\) or \(H_a\)) posits that the population proportion of residents living in mobile homes is greater than 10% (\(p > 0.10\)). It's important to note that the alternative hypothesis is what we hope to conclude if we reject the null hypothesis.
Proportion
The concept of proportion is integral to many statistical tests, especially when dealing with categorical data. A proportion refers to the fraction of items in a category out of the total number of items. It can be expressed as a percentage, fraction, or decimal. In this scenario, the proportion is the quantity we are testing 鈥� specifically, the proportion of people living in mobile homes in the community. If the proportion is indeed greater than 10%, as suggested by the alternative hypothesis, the statistical test will process the collected data to determine whether there is sufficient evidence to support this claim.

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Most popular questions from this chapter

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