Math Problem Statement

You are the store manager of Brand Factory in Mumbai. In the past, you observed that customer arrivals and purchases go up significantly during the sales season compared to regular days in your store. At the same time, it is observed that the customers get irritated while standing at the billing counter. As a store manager, you have counters and necessary actions like involving more staff, opening additional billing counters, and managing the crowd during the sales season. Irrespective of all the arrangements, the customers remain dissatisfied. You wanted to know if the customer's irritation is due to the duration of waiting time. You want to check if the waiting time at the billing counter has changed during the sales season to that of the previous month's average waiting time of 4.5 minutes and a standard deviation of 1.2 minutes. To resolve this business problem, you selected a sample of 35 case points at the billing counter for 1 hour (The data is given in the annexure below). Use this sample information to determine whether there is evidence at the 0.05 significance level that the population mean waiting time at the billing counter has changed in the sales season from the previous month's average waiting time of 4.5 minutes.

Solution

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
One-sample t-test
Sampling

Formulas

t-test formula: t = (x̄ - μ₀) / (s / √n)

Theorems

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Suitable Grade Level

College Level