what is the critical value of 0.02 assuming two tail test
The correct answer and explanation is:
✅ Correct Answer: ±2.33
📘 Explanation (Two-Tailed Test with α = 0.02)
In hypothesis testing, critical values determine the boundaries of the rejection region(s) for a specified level of significance (α). These values depend on:
- Whether the test is one-tailed or two-tailed
- The significance level (α)
- The underlying distribution (often standard normal for z-tests)
🔹 Step-by-Step Breakdown:
1. Two-Tailed Test
For a two-tailed test, the significance level is split between both tails of the standard normal distribution.
Given:
- Total α = 0.02
- Each tail = α/2 = 0.01
2. Use of the Z-distribution (Standard Normal)
We’re assuming a z-test, which uses the standard normal distribution (mean = 0, SD = 1).
We now find the z-scores that leave 0.01 in the lower tail and 0.01 in the upper tail, leaving 0.98 in the middle.
3. Using Z-tables or Calculator
Look up the z-score for area = 0.99 (since you want 1% in the upper tail).
From standard z-tables or calculators:
- z ≈ 2.33
Because it’s a two-tailed test, the critical values are both positive and negative:
- ±2.33
🎯 Interpretation:
If your test statistic (z) is:
- Less than −2.33 or
- Greater than +2.33
→ then you reject the null hypothesis at the 0.02 level of significance.
If the z falls between −2.33 and +2.33, then you fail to reject the null.
📌 Summary:
- Significance level (α): 0.02
- Tail type: Two-tailed
- Critical values: −2.33 and +2.33
- These define the cutoff points for rejecting the null hypothesis.