To calculate the chi-square test statistic for goodness of fit, we need to follow these steps:

1. Determine the expected frequency: Betty expected 20 visitors each day, so the expected frequency for each day is 20.

2. Write the observed frequencies: From the dataTo calculate the chi-square test statistic for goodness of fit, we need to follow these steps:

3. Determine the expected frequency: Betty expected 20 visitors each day, so the expected frequency for each day is 20.

4. Write the observed frequencies: From the

   • Tuesday: 28
   • Wednesday: 20
   • Thursday: 18
   • Friday: 14

5. Apply the chi-square formula: The chi-square statistic is calculated using the formula: $\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$ where:

   • $O_i$ is the observed frequency for each category (each day).
   • $E_i$ is the expected frequency for each category (20 visitors per day in this case).

   We compute this for each day:

   • Tuesday: $\frac{(28 - 20)^2}{20} = \frac{64}{20} = 3.2$
   • Wednesday: $\frac{(20 - 20)^2}{20} = \frac{0}{20} = 0$
   • Thursday: $\frac{(18 - 20)^2}{20} = \frac{4}{20} = 0.2$
   • Friday: $\frac{(14 - 20)^2}{20} = \frac{36}{20} = 1.8$

6. Sum the values: $\chi^2 = 3.2 + 0 + 0.2 + 1.8 = 5.2$

So, the chi-square test statistic is 5.2.

Answer: A.) 5.2

Would you like more details or have any questions? Here are some related questions to expand on this:

1. What is the critical value for this chi-square test at $\alpha = 0.10$?
2. How would the test result differ with an alpha of 0.05?
3. What are the degrees of freedom in this problem?
4. How do we interpret the result of a chi-square goodness of fit test?
5. Can this chi-square test be applied to larger datasets, and how does it scale?

Tip: For a chi-square test, the degrees of freedom are usually calculated as the number of categories minus one.