he test statistic of

zequals

1.83
 
is obtained when testing the claim that

pgreater than

0.3.

Using a significance level of

alpha

equals0.10

​, 

should we reject

Upper H 0
 
or should we fail to reject

Upper H 0

​?

We are conducting a hypothesis test for a population proportion with the following information:

- Test statistic \( z = 1.83 \)
- Significance level \( \alpha = 0.10 \)
- The claim is that \( p > 0.3 \), meaning we are performing a **right-tailed test**.

### Hypotheses:
- Null hypothesis: \( H_0 \): \( p \leq 0.3 \)
- Alternative hypothesis: \( H_a \): \( p > 0.3 \)

### Step 1: Find the critical value
For a right-tailed test at a significance level of \( \alpha = 0.10 \), the critical z-value can be found using a standard normal distribution table or calculator. 

The z-critical value for \( \alpha = 0.10 \) is approximately **1.28**.

### Step 2: Compare the test statistic to the critical value
- The test statistic is \( z = 1.83 \).
- The critical value is \( z_{critical} = 1.28 \).

Since \( 1.83 > 1.28 \), the test statistic falls in the **rejection region**.

### Step 3: Conclusion
Because the test statistic exceeds the critical value, we **reject the null hypothesis** \( H_0 \) at the 0.10 significance level. This means there is sufficient evidence to support the claim that \( p > 0.3 \).

### Do you want details on any part of the explanation?

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Here are 5 related questions you might find helpful:

1. What is the process for conducting a hypothesis test for a proportion?
2. How do you calculate a test statistic for proportions?
3. What does it mean to reject the null hypothesis?
4. How does the significance level \( \alpha \) affect the hypothesis test decision?
5. How do you interpret p-values in hypothesis testing?

**Tip:** In hypothesis testing, a larger significance level (like 0.10) increases the likelihood of rejecting the null hypothesis.

The test statistic z = 1.83 is obtained when testing the claim that p > 0.3. Using a significance level of α = 0.10, should we reject H0 or fail to reject H0?

This problem explores hypothesis testing for a population proportion, testing the claim p > 0.3 using a test statistic z = 1.83 and significance level α = 0.10. Learn how to find the critical value, compare the test statistic, and decide whether to reject the null hypothesis.

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