What is the z for a 960 confidence interval estimation Use E

What is the z for a 96.0% confidence interval estimation? Use Excel and round your answer to three decimal places.

Solution

The 1-alpha rule should be used for 1-sided bounds whereas the 2-alpha rule should be used for 2-sided confidence intervals. The procedure we use to find the z-scores (corresponding to a particular confidence level) will depend on how our particular z-table is set up. In general there are two types of z-tables: those that give left tail areas and those that give right tail areas.

LEFT TAIL Z-TABLE:

For a Two-Sided confidence Interval with confidence level (100 - ?)%, use z-table to find the z-score corresponding to the probability (100 - ?/2)%. So for a 96% confidence level we would need to find the z-score corresponding to (100 - 2)% = .98. We should get a z-score close to 2.053. If not, we probably have a right tail z-table.

For a One-Sided upper/lower confidence bound with confidence level (100 - ?)%, use z-table to find the z-score corresponding to the probability (100 - ?)%. So for a 96% confidence level we would need to find the z-score corresponding to (100 - 4)% = .96. we should get a z-score close to 1.750.

RIGHT TAIL Z-TABLE:

For a Two-Sided confidence Interval with confidence level (100 - ?)%, use z-table to find the z-score corresponding to the probability ?/2%. So for a 96% confidence level we would need to find the z-score corresponding to 2% = .02. We should get a z-score close to 2.053.


For a One-Sided upper/lower confidence bound with confidence level (100 - ?)%, use z-table to find the z-score corresponding to the probability ?%. So for a 96% confidence level we would need to find the z-score corresponding to 4% = .04. We should get a z-score close to 1.750.

IMPORTANT: A z-table may be used in two ways: to find a probability corresponding to a z-score and to find a z-score corresponding to a probability.