Q. Find zα/2 for α=0.13.zα/2=□ (Round to two decimal places as needed.)
Understand the problem: Understand the problem.We need to find the z-score zα/2 that corresponds to an alpha level of 0.13 for a two-tailed test. This means we are looking for the z-score where the area in each tail of the standard normal distribution is 0.13/2, since the total area for both tails must add up to α.
Calculate α/2: Calculate α/2.To find the z-score for the two-tailed test, we first need to divide α by 2 because the alpha level is split between the two tails of the distribution.α/2=0.13/2=0.065
Use z-table: Use the standard normal distribution table.We will use the standard normal distribution table (z-table) to find the z-score that corresponds to an area of 0.065 to the left of the z-score. Since the table typically gives the area to the left of the z-score, we need to find the value that corresponds to 1−0.065=0.935, because we want the area in the right tail to be 0.065.
Find z-score: Find the z-score from the table.Looking at the z-table, we find the closest area to 0.935 and then identify the corresponding z-score. The z-score that corresponds to an area of 0.935 is approximately 1.51.
Round z-score: Round the z-score to two decimal places.The z-score we found is already at two decimal places, so no further rounding is necessary.zα/2=1.51
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