Project 4 Hypothesis Test: Purpose Of This Project

Project 4 Hypothesis Testthe Purpose Of This Project Is Toconduct A H

The purpose of this project is to conduct a hypothesis test to test a published claim. You will conduct either a test of the population mean or a test of the population proportion.

Find a published article that makes a claim. You may want to find a statement related to the data from an earlier project. Collect data, at least 15 values or conduct a poll with 20 subjects to test the claim. You can use data from a previous project to test the claim.

Paper For Above instruction

Hypothesis testing is a fundamental aspect of inferential statistics, enabling researchers and analysts to make informed decisions about population parameters based on sample data. This project centers on scrutinizing a published claim using hypothesis testing methods—either by testing a population mean or a population proportion—depending on the nature of the claim and data available.

The first step involves selecting a credible published article that asserts a specific claim stemming from research, statistical studies, or surveys. The claim should be measurable through data and testable via statistical hypothesis testing. For example, the claim might state that "the average amount of sleep for college students exceeds 7 hours" or "more than 60% of consumers prefer brand A over brand B." Once the claim is identified, it is vital to understand its source and context, ensuring the validity and relevance of the data. Attaching a copy of the claim adds transparency to the research process.

Upon securing the claim, the next step involves collecting relevant data. This data should consist of at least 15 individual observations or responses if analyzing a population mean, or at least 20 responses if analyzing a population proportion. The data collection can be through surveys, polls, or previous datasets from earlier projects, provided they align with the claim to be tested.

After data collection, summary statistics are calculated—namely the sample mean, sample proportion (p-hat), and Standard Deviation or q-hat, as applicable—though work for these computations is not explicitly required in the project instructions. These statistics provide the basis for setting up hypothesis tests.

The core of the project involves formulating hypotheses. The claim is algebraically rewritten to define the null hypothesis (H₀), which represents the default assumption—often that there is no effect or no difference—such as "the average sleep duration is 7 hours" or "the proportion of consumers preferring brand A is 0.60." The alternative hypothesis (H₁) reflects the research question or claim, for example, "the average sleep duration exceeds 7 hours" or "the proportion of consumers preferring brand A is greater than 0.60."

Choosing between a z-test or t-test hinges on the sample size and whether the population standard deviation is known. Typically, a z-test is used when the population standard deviation is known or the sample is large; a t-test is used for smaller samples where the population standard deviation is unknown. Explaining this choice aligns with best statistical practices.

The significance level (α) is selected from common values such as 0.01, 0.05, or 0.10. Once set, the corresponding critical value(s) are identified using statistical tables. These critical values delineate the rejection region for the null hypothesis.

The next step involves calculating the test statistic based on the sample data. The p-value is also computed, providing the probability of observing the data if the null hypothesis is true. The decision rule is then formulated: reject H₀ if the test statistic falls into the critical region or if the p-value is less than α.

Following the decision rule application, a statistical decision is made—either to reject or fail to reject the null hypothesis—and an explanation is given, considering the p-value and critical value. The interpretation of this result involves relaying what this means in the context of the original claim—whether the evidence supports the claim or not.

Finally, the project concludes with a personal reflection on the experience, discussing how much fun it was to conduct the hypothesis test, what was learned, and any insights gained from analyzing the claim and data.

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