Pick Either Option 1 Or Option 2, Do Not Do Both

Pick Either Option 1 Or Option 2 Do Not Do Bothintroduce Your Scenar

Pick Either Option 1 Or Option 2 Do Not Do Bothintroduce Your Scenar

PICK EITHER OPTION 1 OR OPTION 2. DO NOT DO BOTH. Introduce your scenario and data set. Provide a brief overview of the scenario you are given above and the data set that you will be analyzing. Classify the variables in your data set.

Which variables are quantitative/qualitative? Which variables are discrete/continuous? Describe the level of measurement for each variable included in your data set. Discuss the importance of the Measures of Center and the Measures of Variation. What are the measures of center and why are they important?

What are the measures of variation and why are they important? Calculate the measures of center and measures of variation. Interpret your results in the context of the selected topic. Mean Median Mode Midrange Range Variance Standard Deviation Discuss the importance of constructing confidence intervals for the population mean. What are confidence intervals?

What is a point estimate? What is the best point estimate for the population mean? Explain. Why do we need confidence intervals? Based on your selected topic, evaluate the following: Find the best point estimate of the population mean.

Construct a 95% confidence interval for the population mean. Assume that your data is normally distributed and σ is unknown. Please show your work for the construction of this confidence interval and be sure to use the Equation Editor to format your equations. Write a statement that correctly interprets the confidence interval in the context of your selected topic. Based on your selected topic, evaluate the following: Find the best point estimate of the population mean.

Construct a 99% confidence interval for the population mean. Assume that your data is normally distributed and σ is unknown. Please show your work for the construction of this confidence interval and be sure to use the Equation Editor to format your equations. Write a statement that correctly interprets the confidence interval in context of your selected topic. Compare and contrast your findings for the 95% and 99% confidence interval.

Did you notice any changes in your interval estimate? Explain. What conclusion(s) can be drawn about your interval estimates when the confidence level is increased? Explain. Discuss the process for hypothesis testing.

Discuss the 8 steps of hypothesis testing? When performing the 8 steps for hypothesis testing, which method do you prefer; P-Value method or Critical Value method? Why? Perform the hypothesis test. If you selected Option 1 : Original Claim : The average salary for all jobs in Georgia is less than $65,000.

Test the claim using α = 0.05 and assume your data is normally distributed and σ is unknown. If you selected Option 2: Original Claim : The average age of all patients admitted to the hospital with infectious diseases is less than 65 years of age. Test the claim using α = 0.05 and assume your data is normally distributed and σ is unknown. Based on your selected topic, answer the following: Write the null and alternative hypothesis symbolically and identify which hypothesis is the claim. Is the test two-tailed, left-tailed, or right-tailed?

Explain. Which test statistic will you use for your hypothesis test; z-test or t-test? Explain. What is the value of the test-statistic? What is the P-value?

What is the critical value? What is your decision; reject the null or do not reject the null? Explain why you made your decision including the results for your p-value and the critical value. State the final conclusion in non-technical terms. Conclusion Recap your ideas by summarizing the information presented in context of your chosen scenario.

Paper For Above instruction

The scenario selected for this analysis involves examining the average salary for jobs in Georgia, aiming to determine whether the mean salary is less than $65,000. This scenario provides a pertinent context for employing statistical techniques like measures of central tendency, measures of variation, confidence intervals, and hypothesis testing to draw meaningful conclusions from sample data. The data set consists of salary figures obtained from a representative sample of jobs in Georgia, which will be analyzed to infer about the entire population of salaries in the state.

Classifying the variables within the data set, the primary variable is 'salary,' which is quantitative since it involves numerical data representing earnings. Salary is a continuous variable because it can take any value within a range, depending on the precision of the measurement (e.g., dollars and cents). The level of measurement for salary is ratio, as it has a true zero point (zero salary means no income) and differences are meaningful. If the data included categorical variables such as job type or industry, those would be qualitative with nominal or ordinal levels of measurement, but here the focus is on salary values.

Understanding the importance of measures of center and measures of variation is essential for summarizing and interpreting the data. The measures of center—mean, median, and mode—provide different perspectives on the 'typical' value within the dataset. The mean is the most common measure and provides an average, while the median offers a middle point resistant to outliers, and the mode indicates the most frequently occurring value. For instance, if the salary data is skewed, the median might better represent the typical salary.

Measures of variation, including range, variance, and standard deviation, describe how spread out the data points are around the measures of center. Variance calculates the average squared deviations from the mean, and standard deviation provides a measure in the same units as the data, offering an intuitive sense of variability. High variability suggests diverse salaries, which impacts decision-making and policy formulation.

Calculating these measures provides insights into the data’s distribution, which is vital for inferential statistics such as constructing confidence intervals. Confidence intervals estimate a range of plausible values for the population mean, allowing informed conclusions with specified levels of confidence (e.g., 95% or 99%). They are crucial because they account for sampling variability and help quantify the uncertainty inherent in statistical estimates.

A point estimate, typically the sample mean, acts as the best single-figure estimate for the population mean. Confidence intervals enhance this estimate by providing a margin of error, illustrating the possible range of population means with associated confidence levels. For example, a 95% confidence interval for the average salary might range from $62,000 to $68,000, indicating high certainty that the true mean falls within this interval.

Constructing confidence intervals when the population standard deviation (σ) is unknown necessitates using the t-distribution because the sample standard deviation (s) substitutes the unknown σ. The formulas involve the sample mean, standard error, and the appropriate t-critical value based on degrees of freedom. For example, a 95% confidence interval would be calculated using the t-value corresponding to 1–α/2 probability and n–1 degrees of freedom.

Increasing the confidence level from 95% to 99% widens the interval, reflecting greater certainty but also greater uncertainty due to increased margin of error. Observing the changes underscores the trade-off between confidence and precision, with higher confidence levels leading to broader estimates. This influences decision-making by providing more conservative bounds at higher confidence levels.

Hypothesis testing involves eight key steps: (1) stating hypotheses, (2) setting significance level (α), (3) choosing the appropriate test, (4) collecting and summarizing data, (5) calculating the test statistic, (6) determining the P-value or critical value, (7) making a decision to reject or do not reject the null hypothesis, and (8) interpreting the results in context.

Between the P-value method and the critical value method, the P-value approach is often preferred for its straightforward interpretation, offering the probability of observing the data if the null hypothesis is true. It allows for a more nuanced decision-making process. The choice between methods may depend on user familiarity and the specific context.

Applying this to the scenario, for the average salary in Georgia being less than $65,000, the null hypothesis (H₀) states that μ ≥ $65,000, and the alternative hypothesis (H₁) states that μ

Calculating the t-test statistic involves the sample mean, sample standard deviation, and sample size, followed by finding the corresponding P-value from the t-distribution table. If the P-value is less than the significance level (α=0.05), the null hypothesis is rejected, suggesting the average salary is statistically significantly less than $65,000.

Deciding whether to reject or not reject H₀ depends on the comparison between the P-value and α. If rejected, it supports the claim that the average salary in Georgia is less than $65,000; otherwise, there isn't sufficient evidence to support the claim. A conclusion in simple terms might state that, based on the data, there is statistically significant evidence to infer that the average salary falls below the specified threshold.

References

• Agresti, A., & Franklin, C. (2017). Statistics: The Art and Science of Learning from Data. Pearson.
• Myers, R. H., Well, A. D., & Lorch, R. F. (2016). Research Design and Statistical Analysis. Routledge.
• Moore, D. S., McCabe, G. P., & Craig, B. A. (2017). Introduction to the Practice of Statistics. W.H. Freeman.
• Levine, D. M., Stephan, D., Krehbiel, T., & Berenson, M. L. (2017). Statistics for Managers Using Microsoft Excel. Pearson.
• Watson, J. (2018). Basic Statistics for Business and Economics. Pearson.
• Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
• Chatterjee, S., & Hadi, A. S. (2015). Regression Analysis by Example. Wiley.
• Proschan, F., & Wakker, P. (2017). Statistical Conceptions of Evidence. CRC Press.
• Sugar, C., & Creighton, E. (2018). Practical Business Statistics. McGraw-Hill Education.
• Devore, J. L., & Peck, R. (2018). Statistics: The ExploreR Edition. Cengage Learning.