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Answer: At a 5% significance level, we can reject the null hypothesis.
## Explanation The p-value is the probability of obtaining results at least as extreme as the observed results of a hypothesis test, assuming that the null hypothesis is correct. In other words, the p-value is the lowest level at which we can reject the null hypothesis. ### Key Points: - At a 95% confidence level, the significance level (α) is 5% (1 - 95% = 5%) - The p-value of 2.14% is less than the 5% significance level - **Decision Rule**: If p-value ≤ α, reject the null hypothesis ### Analysis: - p-value (2.14%) < α (5%) → **Reject the null hypothesis** - Option A is incorrect because we CAN reject the null hypothesis at 5% significance - Option B is incorrect because while we can reject at 2% significance, this is not the main conclusion from the given information - Option D is incorrect because we have sufficient information to make a conclusion - Option C is correct because at the 5% significance level (which corresponds to the 95% confidence level), we can reject the null hypothesis Therefore, the correct answer is **C**.
Author: Tanishq Prabhu
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A two-tailed hypothesis test at the 95% confidence level has a p-value of 2.14%. This means that:
A
At a 5% significance level, we cannot reject the null hypothesis.
B
At a 2% significance level, we can reject the null hypothesis.
C
At a 5% significance level, we can reject the null hypothesis.
D
We have insufficient information to provide any kind of conclusion.