Describe The 8 Steps In The Hypothesis Testing Process

Describe the 8 steps in the process for hypothesis testing

Explain the decision criteria for rejecting the null hypothesis for both the p-value method and the critical value method. Question 2 Calculations/Values Formulas/Answers Mean (x-bar) Standard Deviation n mu Test Statistic Critical Value P-value 2a. Write the null and alternative hypotheses symbolically and identify which hypothesis is the claim. Then identify if the test is left-tailed, right-tailed, or two-tailed and explain why. 2b. Identify and explain which test statistic you will use for your hypothesis test: z or t? Find the value of the test statistic. Provide your calculations in the cells designated to the right. Explain your answers below. 2c. What is the critical value? Describe the rejection region of this hypothesis test. Provide your calculations in the cells designated to the right. Explain your answers below. 2d. Using the critical value approach, should you reject the null hypothesis or not reject the null hypothesis? Explain. After making your decision, restate it in non-technical terms and make a conclusion about the original claim. 2e. Calculate the p-value for this hypothesis test, and state the hypothesis conclusion based on the p-value. Does this match your results from the critical value method? Provide your calculations in the cells designated to the right. Explain your answers below. Question 3 Calculations/Values Formulas/Answers Mean (x-bar) Standard Deviation n mu Test Statistic Critical Value P-value 3a. Write the null and alternative hypotheses symbolically and identify which hypothesis is the claim. Then identify if the test is left-tailed, right-tailed, or two-tailed and explain why. 3b. Identify and explain which test statistic you will use for your hypothesis test: z or t? Find the value of the test statistic. Provide your calculations in the cells designated to the right. Explain your answers below. 3c. What is the critical value? Describe the rejection region of this hypothesis test. Provide your calculations in the cells designated to the right. Explain your answers below. 3d. Using the critical value approach, should you reject the null hypothesis or not reject the null hypothesis? Explain. After making your decision, restate it in non-technical terms and make a conclusion about the original claim. 3e. Calculate the p-value for this hypothesis test, and state the hypothesis conclusion based on the p-value. Does this match your results from the critical value method? Provide your calculations in the cells designated to the right. Explain your answers below.

Paper For Above instruction

Hypothesis testing is a fundamental process in statistics used to determine whether there is enough evidence to support a specific claim about a population parameter. The procedure involves several clearly defined steps, each critical in ensuring the validity and reliability of the conclusions drawn from the data. This paper delineates the eight steps involved in hypothesis testing, followed by a detailed explanation of the decision criteria for rejecting the null hypothesis using both the p-value and the critical value approaches.

The Eight Steps in Hypothesis Testing

1. State the Hypotheses: The initial step involves formulating the null hypothesis (H₀), which typically states no effect or no difference, and the alternative hypothesis (H₁ or Ha), which indicates the presence of an effect or difference. These hypotheses are expressed symbolically, such as H₀: μ = μ₀ and Ha: μ ≠ μ₀, where μ represents the population mean.

2. Set the Significance Level (α): The significance level defines the threshold for deciding whether the observed data are sufficiently unlikely under H₀. Commonly, α is set at 0.05, implying a 5% risk of rejecting the null hypothesis when it is actually true.

3. Collect Data and Calculate Sample Statistics: Data relevant to the hypothesis are collected through sampling. Sample mean (x̄), sample standard deviation (s), and sample size (n) are computed as preliminary statistics for further analysis.

4. Choose the Appropriate Test Statistic: Depending on the sample size and whether the population standard deviation is known, either the z or t statistic is used. The test statistic quantifies the deviation of the sample data from the null hypothesis.

5. Determine the Critical Value(s): Critical values are thresholds derived from the standard normal distribution (z-scores) or the t-distribution, corresponding to the significance level and the type of test (left-tailed, right-tailed, or two-tailed). These values define the rejection region.

6. Make a Decision - Critical Value Method: The calculated test statistic is compared to the critical value(s). If it falls into the rejection region, H₀ is rejected; otherwise, H₀ is not rejected. The decision is then translated into a non-technical conclusion about the claim.

7. Calculate the P-value: The p-value is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated, assuming H₀ is true. It provides an alternative way to make the decision, independent of the significance level.

8. Make a Decision - P-value Method: The p-value is compared with α. If p ≤ α, H₀ is rejected; if p > α, H₀ is not rejected. The conclusion is articulated in plain language to support or refute the original claim.

Decision Criteria for Rejecting the Null Hypothesis

There are two key approaches to decision making in hypothesis testing:

• Critical Value Method: The test statistic is compared against the critical value(s). If the test statistic exceeds the critical value in the tail(s) of the distribution, the null hypothesis is rejected. For a right-tailed test, rejection occurs if the test statistic is greater than the critical value. Conversely, for a left-tailed test, rejection occurs if the test statistic is less than the negative critical value. In two-tailed tests, rejection occurs if the test statistic falls into either tail beyond the critical value thresholds.
• P-value Method: The p-value represents the probability of obtaining the observed data, or more extreme, given H₀. If the p-value is less than or equal to α, H₀ is rejected; if greater, H₀ is not rejected. This method provides a measure of evidence against H₀; smaller p-values indicate stronger evidence.

Understanding these criteria helps researchers determine whether to accept or reject H₀ with confidence, leading to valid scientific conclusions about the population parameters under study.

Conclusion

Hypothesis testing is an essential statistical tool for making informed decisions based on data. By systematically following the eight steps and applying the decision criteria for both the p-value and critical value methods, researchers can confidently interpret their results, ensuring that their conclusions are statistically sound and meaningful in practical terms.

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