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There is a problem that appears to be based on hypothesis testing regarding the filling of cereal boxes with a weight of 368 grams. The claim being tested is whether or not the average weight of the cereal boxes is indeed 368 grams.

The following hypotheses are provided:
- **Null hypothesis (H0):** μ = 368
- **Alternative hypothesis (H1):** μ ≠ 368

Given Data:
- **Sample size (n):** 8
- **Sample mean (x̄):** 372.5
- **Sample standard deviation (s):** 8.3

There is a table with some of the following details:
- **Test statistic:** Calculated value of 1.28.
- **Critical values:** t = ±2.365 (based on a t-distribution with degrees of freedom df = 7 and a significance level of α = 0.05).

**Questions:**
1. Based on the provided information, the calculated test statistic is **1.28**, which lies within the range of the critical values of t = ±2.365.
2. The question asks whether the null hypothesis should be rejected or not.

**Answer Choices:**
1. Fail to reject the null hypothesis; there is not enough evidence to support the claim.
2. Reject the null hypothesis; there is enough evidence to support the claim.
3. The distribution is too widely spread for a meaningful conclusion.
4. An error occurred in the calculation of the test statistic.

**Analysis:**
The calculated test statistic (1.28) is smaller than the critical value (2.365). Therefore, the test statistic does not fall in the rejection region of the hypothesis test. As a result, we **fail to reject the null hypothesis**. This means there is not enough evidence to suggest that the mean weight of the cereal boxes is different from 368 grams.

Thus, the correct answer is **Option 1: Fail to reject the null hypothesis**.

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Do you want more details on how the test statistic was calculated or any other aspect of hypothesis testing? Here are five related questions that could expand your understanding:

1. How is the test statistic for a t-test calculated?
2. What is the difference between a one-tailed and a two-tailed t-test?
3. How does sample size affect the outcome of hypothesis testing?
4. What is the significance level (α) in hypothesis testing, and why is it important?
5. How are degrees of freedom calculated in a t-distribution?

**Tip:** Always compare your test statistic with critical values to determine whether to reject or fail to reject the null hypothesis.

A hypothesis test is conducted to determine whether the average weight of cereal boxes is 368 grams. The sample size is 8, with a sample mean of 372.5 grams and a standard deviation of 8.3 grams. The test statistic is 1.28, and the critical value is ±2.365. Should the null hypothesis be rejected?

Explore how to conduct a hypothesis test to determine if the average weight of cereal boxes is different from 368 grams. The problem involves using the t-distribution, sample data analysis, and critical values. Suitable for Grades 10-12 students.

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