A Supermarket Is Interested In Finding Out Whether The Mean

Question

A Supermarket Is Interested In Finding Out Wheather the Mean Weekly Sa A supermarket is interested in finding out whether the mean weekly sales volume of Coca-Cola differs based on shelf placement. Specifically, the supermarket wants to compare sales when soft drinks are displayed on the top shelf versus the bottom shelf. They selected ten stores randomly from the chain, with five stores using the top shelf display and five stores using the bottom shelf display. Assuming that the sales volume data are normally distributed with equal population variances, the analysis aims to determine the degrees of freedom for the comparison and the critical values at a significance level of 0.01.

Dr. Jack HW Helper · Accepted Answer

The study conducted by the supermarket involves a comparative analysis of weekly sales volumes of Coca-Cola based on shelf positioning within retail stores. This involves a classic application of inferential statistics, particularly the independent samples t-test, to examine whether the observed differences in means are statistically significant. Key to this analysis are the assumptions of normality and equal variance, which underpin the validity of the t-test in this context. Understanding the Conceptual Framework The core question addresses whether shelf placement influences consumer purchasing behavior, reflected in sales figures. Given the data collection from multiple stores, the supermarket conducts a hypothesis test comparing two independent samples—sales from stores with top shelf placement and those with bottom shelf placement. The null hypothesis posits no difference in mean sales between the two display strategies, while the alternative hypothesis suggests a significant difference exists. Sample Size and Degrees of Freedom In the experimental design, the sample comprises ten stores, divided equally with five in each display configuration. When conducting an independent samples t-test with equal variances assumed, the degrees of freedom (df) are calculated using the formula: $$ df = (n_1 - 1) + (n_2 - 1) $$ where $n_1$ and $n_2$ are the sample sizes for each group. Here, $n_1 = 5$ and $n_2 = 5$, thus: $$ df = (5 - 1) + (5 - 1) = 4 + 4 = 8 $$ Therefore, the degrees of freedom associated with this analysis is 8. Critical Values at Level of Significance $\alpha = 0.01$ To interpret the statistical significance of the calculated t-statistic, critical values are determined based on the level of significance. With a two-tailed test at $\alpha = 0.01$, the threshold values are obtained from standard t-distribution tables or statistical software for df = 8. Using a t-distribution table, the critical t-value for a two-tailed test at $\alpha = 0.01$ an

A Supermarket Is Interested In Finding Out Wheather the Mean Weekly Sa

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