Summary Of Resit Assignment: Composed Of 4 Questions

Summaryresit Assignmentthis Assignment Is Composed By 4 Questions Wit

This assignment is composed of 4 questions, each with multiple subquestions, to assess understanding of various statistical concepts including data description, graphical representation, normal distribution, correlation, sampling, confidence intervals, regression, and hypothesis testing. Answers should be submitted in a readable spreadsheet file (.xlsx or .ods), with all answers clearly identified by question number. All functions used must be visible, and graphs should be properly titled and labeled. Written explanations are required where specified, and all graphical representations must be clear and well-presented.

Paper For Above instruction

Introduction

This paper addresses a comprehensive set of questions designed to evaluate fundamental and applied statistical skills relevant to management analysis. It spans descriptive statistics, data visualization, distribution analysis, correlation, regression modeling, sampling size determination, and hypothesis testing. These skills are vital for informed decision-making in business environments, and this analysis aims to demonstrate proficiency in interpreting data, constructing models, and drawing meaningful conclusions from statistical analyses.

Question 1: Employee Distribution Analysis

The first question revolves around analyzing the distribution of employees across different departments within a company. Given the provided frequencies and relative frequencies, the tasks include calculating missing data and representing the data graphically.

Given data: Frequencies and relative frequencies for departments such as Accounting, Legal, Maintenance, Technology, Human Resources, and Administrative. Some data points are missing, specifically the total number of employees and the relative frequencies for Technology and the total (D).

(a) Calculation of A, B, C, and D:

• Sum of all frequencies equals Total employees, which is calculated as the sum of individual department frequencies.
• Relative frequencies are obtained by dividing each department's frequency by the total number of employees.
• A corresponds to the total number of employees, B and C are the missing frequencies for Technology and Administrative departments, respectively, and D is the total relative frequency, which must total 1.

Calculations:

• Total employees (A): 9 + 12 + 14 + 87 + 15 + B = total (assumed as sum of knowns plus B)
• Relative frequency of Technology (C):
• Relative frequency total (D): 1.0000, which confirms the sum of all relative frequencies.

Using these, the missing values are to be computed explicitly, ensuring the sum of frequencies and relative frequencies aligns with the total count and unity respectively.

(b) Graphical representation:

An appropriate chart such as a pie chart or a bar graph will visually depict the distribution of employees among departments, with each segment labeled and proportionally scaled.

Question 2: Product Data Analysis

This question concerns the analysis of a set of 30 products, with a focus on the variables Price and Manual Labor in minutes.

(a) Histogram:

Create a histogram or stem-and-leaf plot to depict distribution of Prices, with properly labeled axes and titles.

(b) Distribution Classification:

Assess the skewness of Price distribution: whether it is symmetric, positively skewed, or negatively skewed based on the shape of the histogram.

(c) Descriptive Statistics:

• Compute mean, median, and standard deviation of Price, using built-in functions. Results should be clearly shown, with calculations transparent.

(d) Correlation Analysis:

Calculate the correlation coefficient between Price and Manual Labor. Describe whether the relationship is positive, negative, or negligible based on the correlation value.

(e) Regression Modeling:

Decide which variable to use as the independent/explanatory variable based on correlation strength and logical relevance.

(f) Regression Coefficients:

Fit a linear regression model with the selected explanatory variable, extracting slope and intercept.

(g) Prediction:

Use the model to predict Manual Labor for a product costing €4000 or predict Price for 500 minutes labor, based on prior decision.

(h) Graphical Display:

Create a scatter plot with the regression line overlayed, clearly labeled and titled. Include as an image if formatting issues occur.

(i) Random Product Selection:

Propose a method, such as random sampling with software or random number generation, to ensure unbiased selection of six products for display.

Question 3: Wingspan Confidence Interval & Sample Size

Data: Sample of 40 insects’ wingspans, with specified values.

(a) Confidence Interval:

Compute a 95% confidence interval for the population mean wingspan, using the sample mean, standard deviation, and t-distribution, providing the margin of error and interval bounds.

(b) Sample Size Calculation:

Determine required sample size for a 98% confidence interval with a maximum margin of error (E) of 0.2 mm, assuming standard deviation equals the sample's standard deviation. Use the appropriate formula for finite or large populations as applicable.

Question 4: Hypothesis Testing on Tire Durability

Test whether the new tires last longer than the previous version, based on sample data.

(a) Test Type Justification:

Decide whether to use a Z-test or a t-test based on sample size and whether population standard deviation is known.

(b) Test Direction:

Determine if the test should be one-tailed or two-tailed, justifying whether the hypothesis looks for an increase, decrease, or any difference.

(c) Hypotheses Statement:

Formulate null and alternative hypotheses reflecting the research question about increased durability.

(d) Test Execution and Conclusion:

Calculate the test statistic and p-value or rejection region; interpret results in plain language: whether the data supports that the new tires last longer at the 5% significance level, explaining implications.

Conclusion

This comprehensive analysis synthesizes descriptive, inferential, and predictive statistical techniques essential for management decision-making. Proper application of graphical methods, statistical tests, and regression modeling enhances understanding of data behaviors and supports evidence-based strategies, thus advancing managerial insights.

References

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