Determine the expected count under the null hypothesis.

A local retailer currently schedules employees based on the assumption that they serve customers uniformly throughout the week (the same number each day). Management is starting to question this assumption and decides to collect data on the number of customers served each day of the week to perform a Chi-Square goodness-of-fit test at a 5% significance level.

\begin{tabular}{|l|c|c|c|c|c|c|}
\hline
& Monday & Tuesday & Wednesday & Thursday & Friday & Total \\
\hline
Number Served & 40 & 33 & 35 & 32 & 60 & 200 \\
\hline
\end{tabular}

Provided the assumptions of the test are satisfied, determine the expected number of customers served each day under the null hypothesis.



Answer :

To determine the expected number of customers served each day under the null hypothesis, we need to assume that the customers are uniformly distributed across the weekdays. This means that each day should have an equal number of customers, on average.

Given the data:

- Total number of customers served in the week: 200
- Number of days in the week (from Monday to Friday): 5

Under the null hypothesis, each day is expected to have the same number of customers. Therefore, we divide the total number of customers by the number of days to find the expected number of customers per day.

[tex]\[ \text{Expected number of customers per day} = \frac{\text{Total number of customers}}{\text{Number of days}} \][/tex]

Substituting the values:

[tex]\[ \text{Expected number of customers per day} = \frac{200}{5} \][/tex]

[tex]\[ \text{Expected number of customers per day} = 40.0 \][/tex]

So, under the null hypothesis, the expected number of customers served each day is 40.

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