Question

Prop>.5
Z= 2.085144141
P= .0185281093
P^=.6086956522
N=92


Can Hv0 be rejected at the 0.05 level

Answer 1

Do we have enough evidence to conclude that the tax is greater than 0.5

Answer 2

To determine whether to reject the null hypothesis \( H_0 \) at the 0.05 significance level, we need to compare the p-value to the significance level:

1. **Given Data**:
- P-value = 0.0185281093
- Significance level \( \alpha = 0.05 \)

2. **Decision Rule**:
- If the p-value is less than \( \alpha \), we reject the null hypothesis \( H_0 \).
- If the p-value is greater than or equal to \( \alpha \), we fail to reject the null hypothesis.

3. **Comparison**:
- Since \( 0.0185281093 < 0.05 \), we reject \( H_0 \).

In conclusion, you can reject the null hypothesis \( H_0 \) at the 0.05 significance level.

Answer 3

To determine if there is enough evidence to conclude that the tax rate is greater than 0.5, we can reference the results of your hypothesis test. Here’s a structured breakdown:

1. **Hypotheses**:
- Null Hypothesis (\( H_0 \)): The tax rate is less than or equal to 0.5 (\( p \leq 0.5 \)).
- Alternative Hypothesis (\( H_a \)): The tax rate is greater than 0.5 (\( p > 0.5 \)).

2. **Test Details**:
- Z-statistic = 2.085144141
- P-value = 0.0185281093
- Significance Level (\( \alpha \)) = 0.05
- Sample proportion (\( P^ \)) = 0.6086956522
- Sample Size (N) = 92

3. **Decision Rule**:
- Since the p-value (0.0185281093) is less than the significance level (0.05), we reject the null hypothesis.

4. **Conclusion**:
- By rejecting the null hypothesis, you have sufficient evidence to conclude that the tax rate is greater than 0.5.

Therefore, yes, based on the test results, there is enough evidence to conclude that the tax is greater than 0.5.