Solution By Steps

Step 1: Find z alpha/2 for 90% Confidence Level

For a 90% confidence level, alpha = 1 - 0.90 = 0.10.

Since it’s a two-tailed test, alpha/2 = 0.10/2 = 0.05.

Look up the z-value for 0.05 in the standard normal distribution table to find z alpha/2.

Step 2: Find z alpha/2 for 98% Confidence Level

For a 98% confidence level, alpha = 1 - 0.98 = 0.02.

Since it’s a two-tailed test, alpha/2 = 0.02/2 = 0.01.

Look up the z-value for 0.01 in the standard normal distribution table to find z alpha/2.

Step 3: Find z alpha/2 for 88% Confidence Level

For an 88% confidence level, alpha = 1 - 0.88 = 0.12.

Since it’s a two-tailed test, alpha/2 = 0.12/2 = 0.06.

Look up the z-value for 0.06 in the standard normal distribution table to find z alpha/2.

Final Answer

a) For a 90% confidence level, z alpha/2 ≈ 1.645.

b) For a 98% confidence level, z alpha/2 ≈ 2.326.

c) For an 88% confidence level, z alpha/2 ≈ 1.555.

Key Concept

Z Alpha/2

Key Concept Explanation

Z alpha/2 is the critical value in the standard normal distribution that corresponds to the significance level alpha/2 for a two-tailed test. It is used in constructing confidence intervals for population parameters, such as the population mean. The z alpha/2 value helps determine the margin of error in estimating the population parameter.