Question

Test the hypothesis of the following observed frequency table.


Category

f

e
1

60

A

2

65

B

3

75

C

4

80

D



What is the test statistic value?


3.5714


8.2564


12.5646


18.2587

Answer 1

To test the hypothesis using an observed frequency table, we typically compare observed frequencies (f) with expected frequencies (e) using a Chi-square test or similar statistical test.

Given the data:

| Category | Observed Frequency (f) | Expected Frequency (e) |
|----------|------------------------|-------------------------|
| 1 | 60 | A |
| 2 | 65 | B |
| 3 | 75 | C |
| 4 | 80 | D |

However, the expected frequencies (A, B, C, D) are not provided in numerical form, which is necessary to perform a Chi-square calculation.

To proceed, you would typically need the expected frequencies for each category to use the formula:

\[
\chi^2 = \sum \frac{(f_i - e_i)^2}{e_i}
\]

Where \(f_i\) are the observed frequencies and \(e_i\) are the expected frequencies.

**To continue:**
1. Please provide the expected frequencies for categories 1, 2, 3, and 4 so that the Chi-square test statistic can be calculated.
2. If you can provide that, I can help compute the test statistic value based on that data.