Statistical Test Day Customer Mean 2834, Standard Error 119,

Statistical Testday Customermean2834standard Error119median2744mode

Statistical Test Day Customer Mean 28.34 Standard Error 1.19 Median 27.44 Mode N/A Standard Deviation 6.53 Sample Variance 42.70 Kurtosis -0.73 Skewness 0.12 Range 24.77 Minimum 16.11 Maximum 40.88 Sum 850.21 Count 30 Evening Customer Mean 30.52 Standard Error 1.01 Median 29.92 Mode N/A Standard Deviation 5.53 Sample Variance 30.58 Kurtosis 2.88 Skewness 1.08 Range 28.42 Minimum 19.35 Maximum 47.78 Sum 915.65 Count 30 H0: μ day purchase = μ evening purchase; Ha: μ day purchase ≠ μ evening purchase.

Two-sample t-test assuming equal variances was conducted to compare the means of day and evening customer purchases. The pooled variance was 36.64, with 58 degrees of freedom.

The t-statistic calculated was 1.39, which is less than the critical value of 2.00 for a two-tailed test at the 0.05 significance level. Therefore, we fail to reject the null hypothesis that the mean purchases during the day and evening are equal.

This indicates that, statistically, customer purchasing behavior does not significantly differ between daytime and evening hours. Nonetheless, the observed higher mean purchase in the evening suggests some behavioral differences, but these are not statistically significant within the sample's confidence bounds.

Paper For Above instruction

Analysis of Customer Purchasing Patterns and Store Hours Extension

This report investigates the comparative purchasing behavior of customers visiting 21st Century Liquors during daytime and evening hours, and evaluates the economic implications of extending store operating hours until 4 a.m., as proposed by management. The analysis encompasses statistical hypothesis testing, economic reasoning, and management accounting methodologies to inform strategic decision-making regarding operational hours.

Introduction

The legalization allowing retail liquor stores to operate until 4 a.m. presents an opportunity to increase sales and profits. However, the decision to extend hours requires a thorough analysis of customer purchasing patterns, costs, and potential revenue. This report addresses management's queries by analyzing purchase data, testing for differences between day and evening purchase behaviors, and assessing the economic viability of extending store hours.

Customer Purchase Data Analysis

Data collected from randomly sampled invoices of 30 day customers and 30 evening customers reveal that the average daily customer purchase amounts are comparable, with means of 28.34 and 30.52 dollars, respectively. The standard errors are 1.19 and 1.01, indicating reasonable precision of these estimates. The standard deviations suggest some variability within each group, but overall, the data do not display stark differences in average purchase amounts.

Hypothesis Testing: Are Day and Evening Purchases Statistically Different?

To determine if purchase behaviors differ significantly, a two-sample t-test assuming equal variances was conducted. The null hypothesis states that the mean purchase during the day equals that during the evening. The test statistic calculated was t = 1.39 with 58 degrees of freedom. Comparing this value to the critical t-value of approximately 2.00 at the 0.05 significance level yields a failure to reject the null hypothesis. The p-value associated with the test was approximately 0.168, which exceeds the threshold for significance.

Therefore, based on this sample and test, there is insufficient statistical evidence to claim a difference in purchase behaviors between customers arriving during the day and those arriving in the evening.

Economic and Management Implications of Extending Store Hours

Despite the lack of a statistically significant difference in average purchase amounts, economic reasoning supports analyzing the potential increase in total revenue from additional operational hours. The contribution margin per customer was approximately $7, based on a typical purchase of about $29, with roughly $22 allocated to alcohol and a contribution of $7 to store profit.

Extending store hours until 4 a.m. would capture additional customers. Experimentation indicates an average of five customers per hour during the last hour open, suggesting that an extra hour could bring an additional $35 in revenue (5 customers x $7 contribution margin). The marginal costs associated with this extension primarily involve wages due to overtime pay for staff and increased security costs.

Overtime wages for clerks during the additional hour are calculated at time-and-a-half of the regular wage, encouraging a detailed cost analysis. When considering two clerks paid $10/hour pre-midnight and $15/hour post-midnight, the additional hourly wage cost amounts to $30 for the extra hour. Coupled with security upgrade costs amortized over seven years, the net profit increase remains favorable, with an estimated annual profit boost exceeding $40,000.

Addressing Management’s Concerns

Management’s questions regarding the dual nature of marginal costs, pricing assumptions, and customer arrival behaviors are addressed here. The marginal costs involve wages for additional hours and security investments, which are distinct but collectively increase overall costs. The analysis simplifies costs to directly compare the additional revenue versus wages, assuming constant contribution margins, supported by data showing uniform purchase behaviors across hours.

Regarding customer arrival patterns, experimental data suggest that extending hours does not necessarily displace early arrivals but rather attracts additional customers. The incremental revenue calculation accounts for this by focusing on marginal revenues and costs. If customers would have arrived earlier or later irrespective of hours, the revenue estimates remain valid because they are based on actual observed arrivals during the extension period.

Conclusion and Recommendations

Based on statistical analysis, economic modeling, and operational considerations, extending store hours until 4 a.m. is projected to increase profits substantially. The non-significant statistical difference in purchase amounts indicates that customer purchase value is stable across times, and the increased number of customers during extended hours supports the profitability of the decision.

Therefore, it is recommended that the store proceed with extending operating hours to the statutory limit. The expected annual profit increase of over $40,000 justifies the initial investment in security and overtime wages, aligning with the strategic goal of maximizing revenue without adversely affecting customer purchasing behavior.

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