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claim and hypothesis for the PROPORTION. 1. what claim about a proportion from the article did we test 2. what was our null hypothesis for the proportion 3. what was the alternative hypothesis

Based on the information provided in the image, the claim about the proportion from the article was tested regarding the percentage of males in online classes. Here are the answers to your specific questions:

1. **Claim about a Proportion**: The claim tested was that **the proportion of males in online classes is 35%**.

2. **Null Hypothesis (\(H_0\))**: The null hypothesis stated that **the proportion of males in online classes is equal to 35%**, represented as:
   \[
   H_0: p = 0.35
   \]

3. **Alternative Hypothesis (\(H_a\))**: The alternative hypothesis stated that **the proportion of males in online classes is not equal to 35%**, indicating a two-tailed test. It is represented as:
   \[
   H_a: p \neq 0.35
   \]

The test conducted appears to be a two-tailed test for proportions to determine if the true proportion of males significantly differs from the claimed 35%.

Would you like further details on any specific aspect of this hypothesis test?

Here are five related questions for deeper exploration:
1. How do you calculate the test statistic for a proportion hypothesis test?
2. What are the possible outcomes and interpretations for a two-tailed hypothesis test?
3. How do you determine the p-value for a proportion hypothesis test?
4. What conditions must be met for a hypothesis test of proportions to be valid?
5. What is the difference between one-tailed and two-tailed tests?

**Tip:** When testing a proportion hypothesis, ensure that the sample size is large enough for the normal approximation to be valid (generally, \( np \geq 5 \) and \( n(1 - p) \geq 5 \)).

Explore a hypothesis test for the proportion of males in online classes, testing whether the proportion is significantly different from 35%. Learn how to calculate the test statistic, p-value, and interpret the results.

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