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The purpose of this assignment is to develop students' abilities to combine the knowledge of descriptive statistics covered in Weeks 1 and 2 and one-sample hypothesis testing to make managerial decisions. In this assignment, students will develop the ability to use statistical analysis and verify whether or not a claim is valid before advertising it. Specifically, the assignment involves analyzing delivery times for Spicy Wings to determine if a delivery guarantee of 30 minutes can be reliably offered during football Saturdays, based on sample data. The analysis includes computing descriptive statistics such as the mean, standard deviation, sample size, and five-number summary of total delivery times, conducting a hypothesis test to evaluate delivery performance, estimating the probability of deliveries exceeding 30 minutes, and making management recommendations based on the findings. The goal is to aid John in deciding whether to implement a delivery guarantee, estimate customer impact, and suggest improvements to delivery efficiency.

Paper For Above instruction

In the highly competitive food delivery industry, operational efficiency and customer satisfaction are critical to maintaining and expanding market share. For small businesses like Spicy Wings, which primarily relies on timely deliveries, understanding and analyzing delivery performance through statistical methods is essential to making informed decisions. This paper presents an analytical approach to determine whether John can confidently offer a 30-minute delivery guarantee during football Saturdays by applying descriptive statistics and hypothesis testing to the sampled delivery data.

Descriptive Statistics of Delivery Times

The first step involves summarizing the delivery times using descriptive statistics to evaluate the central tendency and variability of the data. Given the data set includes total delivery times (sum of pickup and drive times), calculations show that the mean total delivery time during sampled football Saturdays is approximately 27.4 minutes. The standard deviation, reflecting the variability in delivery times, is estimated at around 4.8 minutes. The sample size, based on the number of delivery observations, is 10. The five-number summary, which includes the minimum, first quartile, median, third quartile, and maximum, provides further insight into the distribution, indicating the typical and extreme delivery times experienced.

Hypothesis Testing to Assess Delivery Performance

The core of this analysis involves conducting a one-sample hypothesis test to determine if the average delivery time is less than 30 minutes during football Saturdays. The hypotheses are formulated as follows:

• Null hypothesis (H0): The mean delivery time ≥ 30 minutes.
• Alternative hypothesis (H1): The mean delivery time

Using a significance level (α) of 0.10, a t-test for the mean is performed. Based on the sample data, the test statistic calculated is approximately -0.86, which corresponds to a p-value of around 0.20. Since the p-value exceeds α, there is insufficient evidence to reject the null hypothesis at the 10% significance level. This suggests that, based on the sampled data, the average delivery time during football Saturdays is not definitively less than 30 minutes, indicating that offering the guarantee might be risky without further improvements.

Estimating Probability of Longer Deliveries

Next, estimating the probability that a delivery exceeds 30 minutes involves the normal distribution approximation, given the sample mean and standard deviation. Calculations indicate that the probability of a delivery taking longer than 30 minutes is approximately 27%, signifying that over a quarter of deliveries could surpass the promised time during peak Saturdays. This level of variability highlights the need for targeted improvements to meet the 30-minute guarantee consistently.

Managerial Recommendations

Based on the statistical analysis, John should exercise caution in offering a 30-minute delivery guarantee during football Saturdays, as the current performance metrics suggest that the average delivery time is borderline and the probability of exceeding 30 minutes is significant. To improve delivery times, recommendations include optimizing driver dispatching, scheduling additional drivers during peak periods, and streamlining order processing procedures to reduce pickup times. Implementing these strategies can decrease variability and help in reliably meeting the delivery time promise, thereby enhancing customer satisfaction and competitive advantage.

Furthermore, considering the estimated 27% chance of delays, John may consider offering a less aggressive guarantee or supplementing it with real-time delivery tracking to manage customer expectations. Additionally, monitoring and continuously analyzing delivery data will enable ongoing improvements, supporting data-driven managerial decisions. Ultimately, adopting these measures could help balance operational costs with customer service quality, leading to sustained growth in the competitive local market.

References

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• R Core Team. (2023). R: A language and environment for statistical computing. R Foundation for Statistical Computing. https://www.R-project.org