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This assignment requires a comprehensive analysis of various statistical data and methodologies applied to management contexts. The tasks encompass demographic surveys, confidence interval estimations, hypothesis testing, regression analysis, and sampling procedures. Each is designed to assess understanding of fundamental statistical concepts in real-world management scenarios, necessitating clear explanations, precise calculations, and relevant interpretations of results. Your work must be individually submitted through Moodle's Turnitin system by the specified deadline, ensuring originality and adherence to academic integrity standards.

Paper For Above instruction

In this paper, I will systematically address the assigned tasks, demonstrating a robust understanding of applied management statistics. The topics include survey design, inferential statistics, hypothesis testing, regression analysis, and sampling techniques, with all interpretations grounded in the given problem contexts.

Question 1: Survey on College Students’ Transportation in Barcelona

The first task is to understand students’ perceptions of Barcelona’s transportation system. The population in this context comprises all college students in Barcelona. Since the survey aims to capture the views of every student, the population is complete and includes every individual enrolled in higher education institutions within Barcelona at the time of data collection.

Regarding sampling, choosing a probability sampling method such as simple random sampling or stratified sampling would be advantageous. Simple random sampling ensures every student has an equal chance of participation, reducing bias and providing a representative snapshot of student opinions. Stratified sampling could enhance the accuracy by dividing students into strata (e.g., faculties or years of study) and sampling within each group proportionally, accounting for potential differences in transportation perceptions across demographic segments.

Thus, a stratified random sample would be optimal to ensure diverse groups within the student population are proportionally represented, leading to more generalizable insights about the overall student body.''

Question 2: Average Delivery Time Analysis

Here, a sample of 25 customers’ delivery times is analyzed to estimate the average with a known population standard deviation, enabling the use of z-tests and confidence intervals.

a) 95% Confidence Interval for Mean Delivery Time

The sample mean (x̄) = 4 days; population standard deviation (σ) = 1.2 days; sample size (n) = 25.

The z-value for 95% confidence level approximately = 1.96.

The standard error (SE) = σ / √n = 1.2 / √25 = 1.2 / 5 = 0.24.

The confidence interval is calculated as:

CI = x̄ ± z SE = 4 ± 1.96 0.24 = 4 ± 0.4704.

Thus, the 95% confidence interval is approximately (3.53 days, 4.47 days).

b) Hypotheses Regarding Manager’s Claim

The manager claims that the average delivery time does not exceed 3 days. The hypotheses are:

• Null hypothesis (H₀): μ ≤ 3 days (the response aligns with the claim).
• Alternative hypothesis (H₁): μ > 3 days (the true mean exceeds 3 days, challenging the claim).

c) Testing the Manager’s Claim at 95% Confidence Level

Calculate the z-statistic:

z = (x̄ - μ₀) / (σ / √n) = (4 - 3) / 0.24 ≈ 1 / 0.24 ≈ 4.17.

Compare z to critical value (1.645 for one-tailed test at 95%). Since 4.17 > 1.645, we reject H₀.

The data provides significant evidence that the average delivery time exceeds 3 days, thus invalidating the manager’s claim at the 5% significance level.

d) Conclusion

Based on the hypothesis test, there is strong statistical evidence to reject the manager's claim. The average delivery time is statistically significantly greater than 3 days, indicating the need for process improvements to meet the delivery expectations.

Question 3: Parental Skill Study and Confidence Interval

The study assesses weekly television viewing hours among children aged 6-11 in Barcelona. The sample size is 100, with a mean of 28 hours and known standard deviation of 5 hours.

a) Estimating the Population Mean with 99% Confidence

Since the population standard deviation is known, the z-distribution applies. The z-value for 99% confidence ≈ 2.576.

Standard error (SE) = σ / √n = 5 / √100 = 5 / 10 = 0.5.

The confidence interval is:

CI = 28 ± 2.576 * 0.5 = 28 ± 1.288.

Thus, the 99% confidence interval for the average weekly TV viewing time is approximately (26.71 hours, 29.29 hours).

b) Conclusion

The interval suggests that the true mean television viewing time for all children in Barcelona is likely between approximately 26.7 and 29.3 hours per week with 99% confidence. This information can guide parental and educational interventions aimed at reducing screen time.

Question 4: Regression Analysis of Income and Work Experience

A regression analysis explores the relationship between annual income and work experience, with the regression results indicating a strong positive correlation (Multiple R = 0.93) and an R² of 0.86, meaning 86% of the variability in income is explained by work experience.

a) Variables and Correlation

The independent variable (predictor) is work experience (in years), while the dependent variable (outcome) is annual income (in 1000 euros). The very high correlation suggests a strong linear relationship, implying that as work experience increases, income tends to increase proportionally.

b) Interpretation of R Square

R² = 0.86 signifies that 86% of the variation in annual income among the sample is accounted for by the linear relationship with work experience.

c) Regression Model and Coefficients

The regression equation is:

Income = 17.351 + 1.362 * Work Experience

Interpreting the coefficients:

• Intercept (17.351): The estimated baseline income when work experience is zero.
• Slope (1.362): For each additional year of work experience, the annual income increases by approximately 1,362 euros.

d) Estimating Income for 15 Years of Experience

Applying the model:

Income = 17.351 + 1.362 * 15 = 17.351 + 20.43 ≈ 37.78 (thousand euros)

Therefore, a person with 15 years of experience is expected to earn about 37,780 euros annually.

Additional: Sampling of Smartphone Models

Using simple random sampling with the provided random number table, I selected 10 unique smartphone models from the larger dataset. Starting from a specified position, I mapped each random number to a model number in the list, ensuring no duplicates and maintaining randomness. The sampled models are:

• Apple iPhone 7
• Xiaomi Mi 4
• Samsung Galaxy S8
• LG G4
• HTC Desire 622G
• Sony Xperia Z5
• Apple iPhone 6S Plus
• Samsung Galaxy J7
• Xiaomi Redmi Note 3
• LG G6

This sampling ensures representativeness in evaluating the performance characteristics of smartphone models for further analysis.

Conclusion

The applied analyses demonstrate comprehensive utilization of statistical tools for management decision-making. Confidence intervals provide estimates of population parameters, hypothesis testing assesses claims against evidence, regression quantifies relationships, and proper sampling procedures ensure representativeness. These methods collectively support informed strategies in management practice, emphasizing data-driven solutions and meticulous interpretation of results.

References

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• Montgomery, D. C., Peck, E. A., & Vining, G. G. (2012). Introduction to Linear Regression Analysis. Wiley.
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