Decision Making Using One Sample Hypothesis Testing Assignme

Decision Making Using One Sample Hypothesis Testingassignment Steps S

Decision-Making using One-Sample Hypothesis Testing Assignment Steps · Show research on the matter that is properly cited and referenced according to APA with references · Create a substantive message would include a personal or professional experience as it relates to the particular theory, please provide examples. Word count of each substantive participation words of each one of the following subjects: 1. Example of a one tailed statistical hypothesis for one-sample data 2. Example of a two tailed statistical hypothesis for one-sample data 3. Example of Type I errors and evaluate the choice of significance levels. 4. Example of Type II errors and evaluate the choice of significance levels. 5. Example of p-value method to make rejection/non-rejection decisions for evaluating the claims about means, proportions, and standard deviations. 6. Example on how claims made by businesses can be validated. 7. Example on how to apply the concepts to validate some simple claims such as the mean time to arrive at work 8. The Week Four Payment Time Case study assignment asks you to use a dataset to apply the concepts of sampling distributions and confidence intervals to make management decisions. Give an example of how the sampling and confidence intervals can help in making decisions in your personal or professional life.

Decision-making is a fundamental process in both personal and professional contexts, often relying on statistical methods to infer insights from data. One of the critical techniques employed is hypothesis testing, which allows decision-makers to evaluate claims about a population parameter based on a sample. This paper explores various aspects of one-sample hypothesis testing, including the formulation of hypotheses, understanding potential errors, and applying the p-value method, alongside practical examples and reflections from personal experience.

1. Example of a one-tailed statistical hypothesis for one-sample data

A one-tailed hypothesis test examines whether a parameter is greater than or less than a specified value. For instance, suppose a manufacturer claims that the average weight of their product is at least 500 grams. A researcher tests this claim with the null hypothesis (H₀): μ ≥ 500 grams, against the alternative hypothesis (H₁): μ

2. Example of a two-tailed statistical hypothesis for one-sample data

A two-tailed hypothesis test assesses if a parameter differs from a specific value, regardless of the direction. For example, detect if a new teaching method affects average test scores. Null hypothesis (H₀): μ = 75, and alternative hypothesis (H₁): μ ≠ 75. Here, the interest is in identifying whether the mean score is significantly different from 75, either higher or lower. This approach is suitable when deviations in either direction are of concern, ensuring a comprehensive evaluation of the claim.

3. Example of Type I errors and evaluate the choice of significance levels

A Type I error occurs when a true null hypothesis is incorrectly rejected. For example, concluding that a new advertising campaign increases sales (rejecting H₀) when, in fact, it does not. The significance level (α), commonly set at 0.05, defines the maximum risk of making a Type I error. Choosing a lower α (e.g., 0.01) reduces the probability of this error but increases the risk of Type II errors. In a professional context, balancing these errors depends on the consequences of false positives versus false negatives, influencing decision thresholds.

4. Example of Type II errors and evaluate the choice of significance levels

A Type II error is failing to reject a false null hypothesis. For example, if a drug trial concludes the drug has no effect when it actually does, a Type II error has occurred. The probability of a Type II error (β) is inversely related to the power of the test. A higher significance level increases the test's power, reducing Type II errors. Conversely, stringent significance levels (lower α) may increase Type II errors, underscoring the importance of selecting an appropriate α based on the stakes involved in the decision.

5. Example of p-value method to make rejection/non-rejection decisions for evaluating the claims about means, proportions, and standard deviations

The p-value method calculates the probability of observing a test statistic as extreme as, or more extreme than, the actual value, assuming the null hypothesis is true. For instance, testing whether the average customer satisfaction score exceeds 80, suppose the calculated p-value is 0.03. Since 0.03

6. Example on how claims made by businesses can be validated

Businesses often make claims about product efficacy or customer satisfaction that require validation through statistical testing. For example, a company claims that their product reduces manufacturing defects to less than 2%. A sample of 200 units shows a defect rate of 1.5%. Conducting a hypothesis test (H₀: defect rate ≥ 2%; H₁: defect rate

7. Example on how to apply the concepts to validate some simple claims such as the mean time to arrive at work

To validate a claim that the average commute time is 30 minutes, a sample of 50 commuters is analyzed, and the sample mean is found to be 28 minutes with a standard deviation of 5 minutes. A t-test for the mean can determine if the true average differs significantly from 30 minutes. Setting hypotheses as H₀: μ = 30, and H₁: μ ≠ 30, if the p-value is less than 0.05, the claim can be rejected or accepted based on the data, allowing practical verification of the claim with real-world implications.

8. Using sampling distributions and confidence intervals to make management decisions

Sampling distributions and confidence intervals are instrumental in decision-making. For example, a manager estimating the average delivery time from a subset of shipments can construct a 95% confidence interval. If the interval is narrow around a mean of 5 days, the manager can confidently plan resource allocation. Conversely, a wide interval indicates uncertainty, suggesting the need for further sampling. This approach allows managers to quantify uncertainty and make informed decisions based on statistical evidence, applicable in various professional scenarios.

References

• Agresti, A., & Finlay, B. (2009). Statistical methods for the social sciences (4th ed.). Pearson.
• Bishop, Y. M. M., Fienberg, S. E., & Holland, P. W. (2007). Discrete multivariate analysis: Theory and practice. Springer.
• Cornfield, T. (2014). Applied statistics in business: A primer. Wiley.
• Lehmann, E. L., & Romano, J. P. (2005). Testing statistical hypotheses (3rd ed.). Springer.
• Montgomery, D. C. (2017). Design and analysis of experiments. Wiley.
• Peck, R., & Devore, J. (2013). Statistics: The exploration and analysis of data (4th ed.). Brooks/Cole.
• Sullivan, M. (2012). Essentials of statistics: A decision-making approach. Pearson.
• Wilkinson, L., & Task Force on Statistical Inference. (1999). Statistical methods in psychology journals: Guidelines and explanations. American Psychologist, 54(8), 594–604.
• Zar, J. H. (2010). Biostatistical analysis (5th ed.). Pearson.
• Upton, G., & Cook, I. (2008). Choosing and using statistics: A biologist's guide. Wiley.