Staff Details ID Service Years MF Positions Salary In 2004

Staffdetailsidserviceyrsmfpositionsalary In 2004000current Salar

Staff details including ID, service years, gender, position, salary in 2004, current salary, age, tertiary qualification, location, and professional status are provided. The data contains repeated and unstructured entries about staff demographics, salaries, qualifications, and locations across different regions, including Wellington, Head Office, Dunedin, Christchurch, and Auckland. Additionally, there are statistical questions involving normal distribution, a design of experiments scenario, and sampling method descriptions. The core assignment is to analyze this data and related statistical and methodological questions, including sketching normal curves, calculating probabilities, designing experiments, describing sampling methods, and applying statistical software.

Paper For Above instruction

This paper addresses the comprehensive analysis of staff data, probabilistic modeling, experimental design, and sampling methods, employing principles of statistics and research methodology.

Data overview and descriptive analysis

The provided staff dataset encompasses essential demographic information such as ID numbers, service years, gender, position titles, salaries in 2004 and current, ages, tertiary qualifications, locations, and professional statuses. The dataset exhibits heterogeneity across regions, with entries from Wellington, Head Office, Dunedin, Christchurch, and Auckland, including various professional and trade qualifications. The data is unstructured with repetitions, and clarity is essential before any analytical procedures.

A descriptive analysis reveals that salaries have increased since 2004, with current salaries showing variability aligned to qualifications and region. Service years range from early career entries to senior staff, and ages span from early 20s to 60s. The distribution of qualifications indicates a majority holding higher degrees or bachelor’s degrees, particularly within professional and specialist roles.

Probabilistic modeling of waiting times

The call center waiting time data suggests a normal distribution characterized by a mean of 2.5 minutes and a standard deviation of 1.7 minutes. Sketching the probability density function (PDF) of this distribution can visually support further calculations.

Question 1: The probability that a randomly selected caller waits longer than 3 minutes is computed using the z-score formula:

\[ z = \frac{x - \mu}{\sigma} = \frac{3 - 2.5}{1.7} \approx 0.29 \]

Using Z-tables, \( P(Z > 0.29) = 1 - P(Z

Question 2: For the wait time between 1 and 2 minutes:

Calculate z-values:

\[ z_1 = \frac{1 - 2.5}{1.7} \approx -0.88, \quad z_2 = \frac{2 - 2.5}{1.7} \approx -0.29 \]

Then:

\[ P(1

This indicates about 19.65% of callers wait between 1 and 2 minutes.

Question 3: To find waiting time exceeding 30%, find the 70th percentile:

\[ P(X > A) = 0.30 \Rightarrow P(Z > (A - 2.5)/1.7) = 0.30 \]

From z-tables:

\[ (A - 2.5)/1.7 = 0.5244 \]

\[ A = 2.5 + 1.7 \times 0.5244 \approx 3.39 \]

Thus, 30% of callers wait longer than approximately 3.39 minutes.

Experimental design scenario

Question 4: An experiment can be designed to test the effect of glue type (three levels: Glue A, Glue B, Glue C) and binding type (two levels: paperback, hardback) on bookbinding strength. A factorial design with 3 × 2 = 6 treatment combinations is appropriate, with multiple samples under each combination to account for variability. The diagram would depict a 2x3 factorial matrix with treatment groups at each intersection, illustrating the independent factors and levels.

Question 5: The factors are ‘Type of Glue’ and ‘Type of Binding’. Treatments include all combinations:

- Glue A with paperback

- Glue A with hardback

- Glue B with paperback

- Glue B with hardback

- Glue C with paperback

- Glue C with hardback

The primary response variable is 'binding strength,' measured in units such as force needed to open or tear the binding, assessed via standardized mechanical testing.

Sampling design and methods

Question 6: Using statistical software (e.g., R, SPSS), a simple random sample of 30 workers from the StaffDetails dataset can be generated with functions like `sample()` in R. The software screen will display the command and output with IDs selected randomly, for example, IDs 102, 205, 312, etc.

Question 7: Other sampling methods include stratified sampling and systematic sampling.

- Stratified sampling divides the population into subgroups (strata) based on characteristics like region or qualification, then randomly samples within each. Advantages include increased precision and representativeness; disadvantages involve complexity and need for detailed population information.

- Systematic sampling selects every k-th individual from a ordered list after a random start. Advantages include simplicity and speed; disadvantages occur if there is periodicity in the list, which can bias the sample.

In conclusion, this analysis integrates staff data examination, probabilistic assessment of waiting times, experimental machinery and design, and sampling methodologies, reflecting a multilevel application of statistical and research principles.

References

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  • Montgomery, D. C. (2017). Design and Analysis of Experiments. John Wiley & Sons.
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  • Buttons, K. (2019). Quantitative Methods for Business. John Wiley & Sons.
  • Ott, R. L., & Longnecker, M. (2015). An Introduction to Statistical Methods and Data Analysis. Cengage Learning.
  • ISO 9001:2015 - Quality management systems — Requirements.
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