Willow Run Outlet Mall Has Two Haggar Outlet Stores 439489

The Willow Run Outlet Mall Has Two Haggar Outlet Stores One Located O

The Willow Run Outlet Mall has two Haggar Outlet Stores, one located on Peach Street and the other on Plum Street. The two stores are laid out differently, but both store managers claim their layout maximizes the amounts customers will purchase on impulse. Data collected from customers at these stores recorded the amounts spent more than planned during each visit: for Peach Street, a sample of ten customers reported spending amounts of $17.58, $19.73, $12.61, $17.79, $16.22, $15.82, $15.40, $15.86, $11.82, and $15.85. For Plum Street, fourteen customers reported spending amounts of $18.19, $20.22, $17.38, $17.96, $23.92, $15.87, $16.47, $15.96, $16.79, $16.74, $21.40, $20.57, $19.79, and $14.83. The goal is to determine whether there is a statistically significant difference in the average impulse purchase amounts between the two stores.

Paper For Above instruction

The question at hand involves comparing the mean amounts of impulse spending between two different store locations within the same outlet mall. Since the data involves two independent samples—customers at Peach Street and Plum Street stores—and the variances of these samples are not assumed to be equal, a t-test for independent means with unequal variances (Welch’s t-test) is appropriate. This statistical method allows us to test whether the difference in mean impulse spending between the two stores is statistically significant at a predetermined significance level, in this case, 0.01.

To understand the significance of the results, it helps to grasp how the t-test functions. Unlike a single-sample t-test, which compares the mean of a sample to a known or hypothesized population mean, an independent samples t-test compares two separate sample means to see if they are significantly different from each other. When variances or sample sizes differ markedly between the two groups, Welch's t-test adjusts the calculation to account for these disparities, providing a more reliable significance test.

The data collected involves ten customers at Peach Street, with impulse purchase amounts averaging around a certain value, and fourteen customers at Plum Street, with their own average. The key steps involve calculating the mean and standard deviation of each sample, then applying the t-test formula for unequal variances. This calculation considers differences in sample sizes and variances, resulting in a t-statistic and an associated degrees of freedom, which together determine the p-value—that is, the probability of observing such a difference, or a more extreme one, if there truly is no difference in the population means.

In statistical analysis, the null hypothesis (H0) posits that there is no difference in the true mean impulse spending between the two stores (μ1 = μ2). The alternative hypothesis (H1) suggests that the means are different (μ1 ≠ μ2). Conducting the t-test involves computing the t-statistic and comparing it against critical values established by the t-distribution for the given degrees of freedom and significance level (0.01). If the p-value is less than this significance level, we reject the null hypothesis and conclude that a significant difference exists.

Based on the calculated data, the t-test results indicate whether the observed difference in sample means is statistically significant or likely due to random variation. If significant, store layout or other factors might influence impulse spending differently. If not significant, the evidence does not support a difference, implying similar impulse spending behaviors at both locations despite different store layouts.

Interpretation of these results is crucial for store managers aiming to optimize layout designs. A significant difference could suggest that layout modifications impact impulse spending, guiding strategic changes. Conversely, a non-significant result might indicate other factors beyond layout influence impulse purchasing behavior.

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