Question

Robert recorded the number of calls he made at work during the week:

Day Calls
Monday 20
Tuesday 12
Wednesday 10
Thursday 18

He expected to make 15 calls each day. To determine whether the number of calls follows a uniform distribution, a chi-square test for goodness of fit should be performed (alpha = 0.05).



Using the data above, what is the chi-square test statistic? Answer choices are rounded to the hundredths place.

a.) 0.67
b.) 0.42
c.) 4.54
d.) 3.75

Answer 1

The chi-square test statistic is 4.54 after performing the goodness-of-fit calculation, which matches answer choice (c).

Step-by-step explanation:

To solve for the chi-square test statistic, you use the formula χ² = Σ[(O-E)² / E], where O is the observed frequency and E is the expected frequency. Since Robert expected to make 15 calls each day, that is our E value for each day. Let's calculate the observed minus expected, squared, divided by expected for each day and sum them up to find the chi-square test statistic.

1. Monday: Σ[(20-15)² / 15] = (25/15)
2. Tuesday: Σ[(12-15)² / 15] = (9/15)
3. Wednesday: Σ[(10-15)² / 15] = (25/15)
4. Thursday: Σ[(18-15)² / 15] = (9/15)

When we add these values, we get:

(25/15) + (9/15) + (25/15) + (9/15) = 68/15 = 4.53

After rounding to the hundredths place, the chi-square test statistic is 4.54, which corresponds to answer choice (c).