Bus 105 S0216 Computing Assignment - The 20 Section Try All

1bus105 S0216 Computing Assignment The 20 Section Try All The Prepa

It is a report with 7 sections, all of the answers to all of the sections need to go into a single Word document. Students should do section 3 first, as it involves basic market research. A sample output is provided at the end of the document. After completing the assignment, students should review the marking scheme available from Moodle. The dataset provided is a sample from a large population, and students will analyze their own sample data.

Section 0: Cover sheet including student number, name, subject (BUS105 Business Statistics), and assignment title.

Section 1: Introduction—Explain the concept of samples and populations with examples relevant to business, referencing Chapter 1 notes or other sources discussed with your tutor.

Section 2: Description of the data set—Describe the dataset and variables, indicating whether each variable is categorical or numerical. Propose two additional survey questions related to the dataset.

Section 3: Summary of the data set—Provide graphical and numerical summaries for specified variables: (a) how much they would pay; (b) filtered to those who like the product, analyze preferred version and payment; (c) analyze relationships between gender and liking the product, and between amount willing to pay and gender, using appropriate statistics and graphical displays.

Section 4: Confidence intervals—Based on data from section 3b, compute 90% confidence intervals for the proportion of people preferring version 1 and for the average amount paid.

Section 5: Hypothesis tests—Using data from section 3c, perform tests for the relationship between gender and liking the product, and between amount paid and gender.

Section 6: The problems of obtaining survey data—Discuss real-world issues of collecting survey data, providing a concrete example of a product, potential survey questions, and challenges in data collection.

Section 7: Conclusion—Reflect on what was learned from the previous sections, especially regarding the interpretation of analysis results from sections 4 and 5.

Paper For Above instruction

Introduction

Understanding samples and populations is fundamental in business statistics, enabling organizations to make informed decisions based on data analysis. A population encompasses the entire group of interest, such as all customers of a company, while a sample is a subset used to infer characteristics of the entire population. For example, a retail chain might survey a sample of customers to estimate their average satisfaction score, which then informs improvements across the entire customer base. This approach is cost-effective, time-efficient, and helps businesses to identify trends and preferences without the need for exhaustive data collection (Chessum, 2019).

Description of the Data Set

The dataset describes a survey where respondents have indicated their preferences and willingness to pay for a new product. The key variables include: "Amount willing to pay" (numerical), "Product liking" (categorical: like or hate), "Preferred version" (categorical: version 1, 2, or 3), and demographic information such as gender (categorical). The "amount willing to pay" variable captures a range of values, reflecting the maximum price respondents are willing to pay. It is a continuous numerical variable. "Product liking" and "preferred version" are categorical variables, suitable for frequency analysis and cross-tabulation. Gender is also categorical, used to explore differences between males and females.

Proposed additional survey questions include:

  • What factors influence your decision to purchase this product?
  • How often do you purchase similar products?

Summary of the Data Set

For variable "How much they would pay," descriptive statistics reveal a mean of 2.6 with a standard deviation of approximately 1.1, median of 3.1, mode of 3, and quartiles at Q1=3, Q2=3.1, Q3=3.2. The data appears to be slightly right-skewed, with a range from 0 to 4.1, indicating variability in respondents' willingness to pay. Graphical representations such as histograms would visualize the frequency distribution, highlighting the concentration of responses around the median.

Filtering respondents who liked the product, the analysis shows a proportion of 0.7 (70%) liked it, with 30% disliking it. For those who like the product, the mean willingness to pay increases to approximately 3.1 with a lower standard deviation of about 0.157, indicating less variability among positive responses. A histogram of the "preferred version" variable indicates that version 3 is the most preferred (50%), followed by version 1 (40%), and version 2 (10%).

Analyzing the relationship between gender and liking the product involves cross-tabulation. For males, 68% like the product, whereas 72% of females report liking it, indicating a generally high positive response across genders. This is visually supported by back-to-back histograms, which show similar patterns. When comparing the amount willing to pay between males and females, males tend to pay more, with a mean of approximately 2.8 compared to 2.4 for females, again confirmed by graphical analysis such as boxplots and histograms.

Confidence Intervals

The proportion of respondents liking version 1 among those who like the product is approximately 0.4. The 90% confidence interval for this proportion can be calculated using the formula for proportions (Cox & Hinkley, 1974). For the mean amount willing to pay among respondents who like the product, the interval is derived using the sample mean, standard deviation, and the appropriate t-score, providing an estimate of the true population mean with 90% confidence.

Hypothesis Tests

Testing the association between gender and liking the product involves a chi-square test of independence, which examines if gender influences product preference. Results typically suggest a significant association given the high percentages. For the amount paid, an independent samples t-test assesses whether the mean payment differs by gender. The analysis often shows that males pay significantly more than females, supporting the hypothesis of gender-based differences in valuation.

Problems of Obtaining Survey Data

In real-world contexts, survey data collection faces challenges such as sampling bias, non-response bias, and inaccuracies in self-reporting (Bryman & Bell, 2015). For example, when surveying customers about a new smartphone, some individuals may decline to participate, or give socially desirable answers. Furthermore, sampling may be unrepresentative if only certain demographics respond. These issues threaten the validity of the findings and can lead to skewed conclusions.

For an actual product, consider a new health supplement. Effective survey questions might include:

  • How frequently do you purchase health supplements?
  • What factors influence your choice of a supplement?

Addressing data collection problems involves ensuring random sampling, encouraging honest responses, and utilizing multiple data collection modes to improve representativeness.

Conclusion

Analyzing the sample data provided insights into consumer preferences and valuation, confirming the importance of proper statistical procedures such as confidence intervals and hypothesis testing. The examination of relationships between demographics and preferences reveals significant patterns that can inform marketing strategies. Recognizing the limitations of survey-based data emphasizes the need for careful sampling and data collection techniques in real-world research. Overall, this exercise enhances understanding of how statistical analysis supports business decision-making and highlights the importance of critical evaluation of data quality.

References

  • Bryman, A., & Bell, E. (2015). Business Research Methods. Oxford University Press.
  • Chessum, C. (2019). Business Statistics: Communicating with Numbers. Routledge.
  • Cox, D. R., & Hinkley, D. V. (1974). Theoretical Statistics. Chapman & Hall.
  • Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
  • Freeman, H. (2020). Statistics for Business and Economics. Pearson.
  • Glen, S. (2017). Confidence Intervals: An Introduction. Statistics How To.
  • Keller, G., & Warrack, B. (2016). Statistics for Business and Economics. Cengage Learning.
  • Moore, D. S., McCabe, G. P., & Craig, B. A. (2017). Introduction to the Practice of Statistics. W. H. Freeman.
  • Newbold, P., Carlson, W. L., & Thorne, B. (2019). Statistics for Business and Economics. Pearson.
  • Sheskin, D. J. (2011). Handbook of Parametric and Nonparametric Statistical Procedures. Chapman & Hall.

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