Given The Sales Data For Weekly Gross Receipts

Given The Following Sales Data For Weekly Gross Receipts Of A Random S

Given the following sales data for weekly gross receipts of a sample of 25 restaurants in an international fast food chain (measured in thousands of dollars):

a) Enter these data into a MINITAB worksheet with a single column titled "Sales." Use the software to select Stat > Basic Statistics > 1-sample t. Complete the dialog to obtain a 95 percent confidence interval for the average weekly sales of all over 8,000 restaurants in the chain.

b) Based on the computed confidence interval, assess whether there is strong evidence to suggest that the average weekly sales of restaurants in this chain are significantly higher than $22,000. Provide an explanation based on your findings.

Paper For Above instruction

This paper explores the statistical analysis of weekly gross receipts in a large international fast food chain, focusing on determining whether the chain's average restaurant sales exceed a specified threshold. Specifically, it discusses the application of the one-sample t-test to a sample of 25 restaurants and interprets the resulting confidence interval to draw conclusions about the entire population of over 8,000 outlets. Furthermore, the paper examines the implications of this analysis in understanding the revenue performance of the chain and evaluates whether evidence supports claims of higher-than-average sales.

To begin, the collection of sales data from a random sample of 25 restaurants provides a basis for inferential statistics. By inputting these data into MINITAB, a statistical software package, and performing a one-sample t-test at a 95% confidence level, the researcher aims to construct a confidence interval for the mean weekly sales of all chain restaurants. The computation involves calculating the sample mean and standard deviation, which serve as estimators for the population parameters. The t-distribution is utilized because of the small sample size and the unknown population variance. The resulting confidence interval offers a range within which the true average weekly sales are likely to fall, with a specified level of confidence.

Assuming the confidence interval obtained is, for example, ($23.5 thousand, $27 thousand), it indicates the estimated mean weekly sales of restaurants in the chain is somewhere between these two values. If the lower bound of this interval exceeds $22 thousand, it provides significant evidence that mean sales are higher than this amount. Consequently, the results would support the hypothesis that the chain’s restaurants are generating more revenue on average than the benchmark amount, which can influence managerial decisions, marketing strategies, and overall corporate evaluation.

Conversely, if the confidence interval includes $22 thousand or falls below it, then there is insufficient evidence to definitively conclude that average weekly sales surpass this figure. This evaluation hinges on whether the interval does or does not include the threshold value of $22 thousand. If the lower limit is below $22 thousand, it suggests that the true average cannot be confidently said to be higher, thus diminishing the strength of evidence supporting higher sales.

From a broader perspective, applying statistical inference in this context allows a company to make data-driven assertions about its performance across thousands of outlets. The reliability of conclusions depends on the sample size, data variability, and the confidence level chosen. Notably, increasing sample size or reducing data variability enhances the precision of the estimate, thereby providing stronger evidence either way.

In practice, such analysis informs strategic decisions regarding marketing, expansion, and operational efficiencies. If the chain indeed maintains a higher average weekly sales, this could justify further investment in its locations or promotional activities. Conversely, if the data suggest only marginal or uncertain gains, the company might reassess its business model or focus on product innovation and customer engagement to boost sales.

In conclusion, analyzing sample data through the one-sample t-test and interpreting confidence intervals is a critical process for evaluating business performance. In the context of a large fast food chain, these statistical tools facilitate an understanding of whether observed sales figures reflect genuine superior performance or are within the range of normal variation. Proper application and interpretation guide managerial decisions and strategic planning, ultimately supporting the company's growth and profitability.

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