Derive one Tail and Two Tail numbers for c = 0.88 or alpha = 0.12.
To derive one-tail and two-tail numbers for a given c-value or α-value, you need to use a standard normal distribution table or a statistical software that provides the z-score values.
Here's how you can derive the one-tail and two-tail numbers for c = 0.88 or α = 0.12:
1. Determine the critical z-value for the given α or c.
- For a given α-value, you need to find the critical z-value that corresponds to the cumulative probability (area under the curve) in one tail. Since α is the significance level, it determines the area in one tail of the distribution.
- If α is equal to 0.12, then the significance level for each tail is α/2 = 0.12/2 = 0.06.
- Use a standard normal distribution table or a statistical software to find the z-value for the cumulative probability of 0.94 (1 - 0.06) or 0.06. This represents the critical z-value that corresponds to a significance level of 0.06 in one tail.
2. Calculate the one-tail number.
- The one-tail number is the value obtained after applying the z-value derived in step 1 to the given c-value.
- Multiply the c-value by the one-tail z-value to calculate the one-tail number.
- For c = 0.88 and the derived z-value (assuming it is 1.55, considering a significance level of 0.06), the one-tail number is 0.88 * 1.55 = 1.364.
3. Calculate the two-tail numbers.
- The two-tail numbers represent the range within which random sample means are likely to fall, accounting for both tails of the distribution.
- Subtract the one-tail number derived in step 2 from the c-value and multiply the result by -1 to get the lower two-tail number.
- Add the one-tail number derived in step 2 to the c-value to get the upper two-tail number.
- For c = 0.88 and the derived one-tail number (1.364), the lower two-tail number is (0.88 - 1.364) * -1 = 0.484 and the upper two-tail number is (0.88 + 1.364) = 2.244.
So, for c = 0.88 or α = 0.12, the derived numbers are:
- One-tail number: 1.364
- Lower two-tail number: 0.484
- Upper two-tail number: 2.244