est the claim that the mean GPA of night students is significantly different than 3.3 at the 0.2 significance level.

The null and alternative hypothesis would be:

H0:p=0.825𝐻0:𝑝=0.825
H1:p≠0.825𝐻1:𝑝≠0.825


H0:p≤0.825𝐻0:𝑝≤0.825


It seems there is some confusion in the hypotheses presented. You're dealing with a hypothesis test regarding the mean GPA of night students and whether it significantly differs from 3.3. This test should be framed around the population mean (\(\mu\)), not the population proportion (\(p\)).

Given that you're testing whether the mean GPA is different from 3.3, the correct null and alternative hypotheses should be:

### Null Hypothesis (\(H_0\)):
\[
H_0: \mu = 3.3
\]
This hypothesis states that the mean GPA of night students is equal to 3.3.

### Alternative Hypothesis (\(H_a\)):
\[
H_a: \mu \neq 3.3
\]
This hypothesis states that the mean GPA of night students is different from 3.3. This is a two-tailed test because you're checking for any significant difference, whether the mean GPA is higher or lower than 3.3.

### Significance Level:
The significance level (\(\alpha\)) is 0.2, which is quite high compared to more common levels like 0.05 or 0.01, indicating a greater tolerance for Type I error.

Would you like to proceed with this information, or do you have any further questions?

---

1. What is the difference between a two-tailed and one-tailed test?
2. How does changing the significance level (\(\alpha\)) impact the hypothesis test?
3. What steps would you take to compute the p-value for this hypothesis test?
4. What is a Type I error in hypothesis testing?
5. How do you interpret the results of a hypothesis test?

**Tip:** In hypothesis testing, always ensure the null and alternative hypotheses are stated correctly to reflect the research question or claim you're testing.

Learn about hypothesis testing for the mean GPA of night students compared to 3.3 with a significance level of 0.2. Understand the null and alternative hypotheses, significance levels, and interpretation of results.

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