Question

multiple choice 4 points
determine the critical value.
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.
frequency table: monday = 40, tuesday = 33, wednesday = 35, thursday = 32,
friday = 60, total = 200
provided the assumptions of the test are satisfied, determine the critical value for the test.
12.59
7.81
5.99
3.84
9.49

Explanation:

Step1: Determine the degrees of freedom

The formula for degrees of freedom in a goodness - of - fit test is \(df = k - 1\), where \(k\) is the number of categories. Here, \(k = 5\) (Monday, Tuesday, Wednesday, Thursday, Friday).
\(df=5 - 1=4\)

Step2: Find the critical value

For a \(\chi^{2}\) test (goodness - of - fit is a \(\chi^{2}\) test) with \(\alpha = 0.05\) (5% significance level) and \(df = 4\), we look up the value in the \(\chi^{2}\) distribution table.
The critical value of \(\chi^{2}\) with \(\alpha=0.05\) and \(df = 4\) is \(9.49\)

Answer:

\(9.49\)