Sure, let's solve this step-by-step.
### Step 1: Set Up the Problem
We are given the observed frequencies (the actual number of visitors) for four different days:
- Tuesday: 18
- Wednesday: 24
- Thursday: 28
- Friday: 30
The expected number of visitors each day is 25.
### Step 2: Recall the Formula for Chi-Squared Test Statistic
The formula for the chi-squared test statistic ([tex]\(x^2\)[/tex]) is given by:
[tex]\[
x^2 = \sum \frac{(O_i - E_i)^2}{E_i}
\][/tex]
where [tex]\(O_i\)[/tex] is the observed frequency and [tex]\(E_i\)[/tex] is the expected frequency for each category [tex]\(i\)[/tex].
### Step 3: Calculate the Chi-Squared Test Statistic
Let's calculate the test statistic by plugging in the given values:
1. For Tuesday:
- Observed ([tex]\(O\)[/tex]): 18
- Expected ([tex]\(E\)[/tex]): 25
[tex]\[
\frac{(18 - 25)^2}{25} = \frac{(-7)^2}{25} = \frac{49}{25} = 1.96
\][/tex]
2. For Wednesday:
- Observed ([tex]\(O\)[/tex]): 24
- Expected ([tex]\(E\)[/tex]): 25
[tex]\[
\frac{(24 - 25)^2}{25} = \frac{(-1)^2}{25} = \frac{1}{25} = 0.04
\][/tex]
3. For Thursday:
- Observed ([tex]\(O\)[/tex]): 28
- Expected ([tex]\(E\)[/tex]): 25
[tex]\[
\frac{(28 - 25)^2}{25} = \frac{3^2}{25} = \frac{9}{25} = 0.36
\][/tex]
4. For Friday:
- Observed ([tex]\(O\)[/tex]): 30
- Expected ([tex]\(E\)[/tex]): 25
[tex]\[
\frac{(30 - 25)^2}{25} = \frac{5^2}{25} = \frac{25}{25} = 1.00
\][/tex]
### Step 4: Sum Up All the Contributions
Now, sum up all the contributions to the chi-squared statistic from the different days:
[tex]\[
x^2 = 1.96 + 0.04 + 0.36 + 1.00 = 3.36
\][/tex]
### Conclusion
The chi-squared test statistic is:
[tex]\[
x^2 = 3.36
\][/tex]
Thus, the chi-squared test statistic, rounded to the nearest hundredth, is [tex]\(3.36\)[/tex].
