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. A sample of ten customers at the Peach Street store revealed they spent the following amounts more than planned: $17.58, $19.73, $12.61, $17.79, $16.22, $15.82, $15.40, $15.86, $11.82, $15.85. A sample of fourteen customers at the Plum Street store revealed they spent the following amounts more than they planned when they entered the store: $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, $14.83. For Data Analysis, a t-Test: Two-Sample Assuming Unequal Variances was used. At the .01 significance level, is there a difference in the mean amount purchased on an impulse at the two stores? Explain these results to a person who knows about the t test for a single sample but is unfamiliar with the t test for independent means.
Paper For Above instruction
The primary objective of this analysis was to determine whether there is a statistically significant difference in the mean amounts spent impulsively by customers at two different Haggar Outlet Stores located within the Willow Run Outlet Mall. Using the collected sample data and an independent samples t-test assuming unequal variances, we examine whether the layout differences at Peach Street and Plum Street stores influence customer spending behavior at a significance level of 0.01.
The data comprises two independent samples: ten customers from the Peach Street store and fourteen customers from the Plum Street store. Each customer’s excess spending amount over their planned expenditure was recorded. The sample means indicated that, on average, Peach Street customers spent approximately $15.29 more than planned, while Plum Street customers spent around $21.55 more. The statistical analysis aimed to determine whether this apparent difference is statistically significant or could have arisen by chance.
The t-test for independent samples with unequal variances is used here because it accounts for the possibility that the two populations have different variances, an assumption often realistic in real-world data. Unlike a single-sample t-test, which compares a sample mean to a known population mean, the independent t-test compares the means from two separate groups. The key outputs of this test include the t-statistic, degrees of freedom, and p-value, which collectively determine whether the observed difference
is significant.
In this case, the calculated t-value was approximately -5.28, with a corresponding p-value less than 0.01 (specifically, less than the 0.01 threshold). The negative t-value indicates that the mean spending at Peach Street was less than Plum Street, but the critical aspect is the p-value. Since the p-value is below the significance level, we reject the null hypothesis that the means are equal, concluding that there is a statistically significant difference in impulsive spending between the two stores.
To interpret this for someone familiar only with a single-sample t-test: the single-sample test compares one group’s mean to a known value, testing if the group’s average differs from that value. The independent samples t-test compares the averages of two different groups directly, determining whether the difference in their means is likely due to chance or represents a real difference. The significant result here suggests that the layout of the stores may indeed influence impulsive customer expenditures, with the Plum Street store prompting higher spending.
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