Find the critical value
za/2 that corresponds to
a=0.12.
Unclear. Typo? Z = .12/2 = .06?
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (.06) and its Z score.
the average cost of a house in a new subdivision is inferential or descriptive?
To find the critical value zα/2 for a given value of α, we need to use a standard normal distribution table or a calculator that provides the cumulative distribution function (CDF) for the standard normal distribution.
For a one-tailed test, we need to find the z-value that leaves α/2 to the left of it. Since α = 0.12, α/2 = 0.12/2 = 0.06.
Looking up the z-value corresponding to a cumulative probability of 0.06 in the standard normal distribution table or using a calculator, we find that the critical value for a = 0.12, or z0.06, is approximately -1.555.
Therefore, the critical value zα/2 that corresponds to a = 0.12 is -1.555.
To find the critical value za/2 that corresponds to a given value of a, we can use a standard normal distribution table or a calculator.
1. Using a standard normal distribution table:
- Step 1: Determine the two-tailed significance level (α/2) based on a. Since a = 0.12, α/2 = 0.12/2 = 0.06.
- Step 2: Look for the closest probability value to α/2 in the middle of the table. In this case, look for 0.0600 or the closest value below it (e.g., 0.0596).
- Step 3: Find the corresponding z-value in the leftmost column of the table. In this case, the z-value is approximately 1.56.
- Step 4: The critical value za/2 is the negative of the z-value from Step 3. Therefore, za/2 ≈ -1.56.
2. Using a calculator (such as Excel or a statistical software):
- Utilize the inverse normal distribution function (also known as the quantile function or the percent-point function) to find the value of za/2 based on a. In this case, enter the equation "=NORM.INV(0.06,0,1)" into a cell in Excel (assuming the standard normal distribution with mean 0 and standard deviation 1 is used). The result will be approximately -1.56.
Therefore, the critical value za/2 that corresponds to a = 0.12 is approximately -1.56.