Question

You must choose a confidence level (probability). Let's assume you want to be 90% confident, so α/2 = 0.05 (or 0.95—your choice). Do reverse lookup in a Z table____ or use Excel function NORM.INV(0.95,0,1) = _____.

Answer 1

The question involves finding a Z-score for a specific confidence level in statistics. For a 90% confidence interval, you look up or calculate the Z-score that leaves 5% in the tail, approximately 1.645. Different commands and tools can be used, including Z-tables, Excel functions like NORM.INV, or calculator commands like invNorm.

Step-by-step explanation:

The question relates to the concept of finding a critical value for a given confidence level using a Z distribution, which is a foundational concept in statistics. You have chosen to be 90% confident, which means you are allowing for a 10% error rate, split equally in the two tails of the normal distribution curve, thus, α/2 = 0.05. To find the Z-score that corresponds to the upper tail (α/2 = 0.05), you can use statistical tools such as a Z-table or computer functions like NORM.INV in Excel or invNorm in a calculator. For a 90% confidence interval, you would be looking for the Z-score that leaves 5% in the upper tail (since the confidence interval is the middle 90%). The Z-score that corresponds to an area of 0.95 to the left (or 0.05 to the right) is approximately 1.645.

Alternatively, if you're looking for the Z-score that cuts off the upper 2.5% (for a different confidence level, like 95%), you would use invNorm(0.975, 0, 1), which would give you a Z-score of approximately 1.96. These calculations are essential for constructing confidence intervals and hypothesis testing in statistics.