Question 1188762
Here's how to perform a goodness-of-fit test to determine if Fei Hung's noodle sales data fits a uniform distribution:

**1. State the Hypotheses:**

*   **Null Hypothesis (H0):** The number of bowls of noodles sold each day follows a uniform distribution.
*   **Alternative Hypothesis (H1):** The number of bowls of noodles sold each day does *not* follow a uniform distribution.

**2. Calculate Expected Frequencies:**

If the distribution is uniform, we expect the same number of bowls sold each day.  Calculate the average number of bowls sold over the week:

(48 + 59 + 44 + 55 + 62 + 67 + 50) / 7 = 55

So, the expected frequency for each day is 55.

**3. Calculate the Chi-Square Statistic:**

The chi-square statistic measures the difference between the observed and expected frequencies. The formula is:

χ² = Σ [(Observed Frequency - Expected Frequency)² / Expected Frequency]

| Day     | Observed (O) | Expected (E) | (O - E)² | (O - E)² / E |
|---------|--------------|--------------|----------|---------------|
| Mon     | 48           | 55           | 49       | 0.891         |
| Tues    | 59           | 55           | 16       | 0.291         |
| Wed     | 44           | 55           | 121      | 2.2           |
| Thurs   | 55           | 55           | 0        | 0             |
| Fri     | 62           | 55           | 49       | 0.891         |
| Sat     | 67           | 55           | 144      | 2.618         |
| Sun     | 50           | 55           | 25       | 0.454         |
| **Total** |              |              |          | **7.345**     |

χ² ≈ 7.345

**4. Degrees of Freedom:**

Degrees of freedom (df) = Number of categories - 1 = 7 - 1 = 6

**5. Compare to Critical Value:**

The critical value given is 12.59 at a 5% significance level.  Our calculated χ² (7.345) is *less* than the critical value (12.59).

**6. Conclusion:**

Since the calculated chi-square statistic is less than the critical value, we *fail to reject* the null hypothesis.  There is not enough evidence at the 5% significance level to conclude that the number of bowls of noodles sold each day does *not* follow a uniform distribution.  In other words, the data is consistent with a uniform distribution.