Question

est the hypothesis of the following observed frequency table.


Category

f

E
1

68

A

2

65

B

3

77

C

4

90

D



What is the critical value?


7.82


9.35


9.49


11.14

Answer 1

To determine the critical value for hypothesis testing with a frequency table, we first need to understand what type of test is being performed. Assuming you are conducting a chi-squared test to compare observed frequencies against expected frequencies, the critical value depends on the degrees of freedom (df) and the significance level (usually α = 0.05).

1. **Calculate the Degrees of Freedom:**
The degrees of freedom for a chi-squared test is calculated as:
\[
df = k - 1
\]
where \( k \) is the number of categories.

In this case, you have 4 categories (E, A, B, C, D). Assuming D is the last category, the total number of categories \( k = 4 \). Therefore,
\[
df = 4 - 1 = 3
\]

2. **Find the Critical Value:**
Once we have the degrees of freedom, we can determine the critical value for a chi-squared distribution at our chosen significance level. For \( df = 3 \) and \( \alpha = 0.05 \) (common level), we can look up the critical value or use a chi-squared table.

The critical value for df = 3 and a significance level of 0.05 is approximately **7.815**. Using standard chi-squared tables or calculators, we find the closest values among your options:

- 7.82
- 9.35
- 9.49
- 11.14

Thus, the appropriate critical value choice given the list of options is **7.82**.

Therefore, assuming a chi-squared test at a significance level of 0.05, the critical value is **7.82**.