Reading a z-score chart

1. Dec 16, 2009

60051

I made sure this chart is identical to the one in my textbook, so there are no discrepancies.

So in the solutions manual, they find alpha by subtracting the confidence coefficient from 1, then dividing that value by 2, and looking up that value in the table.

So for one example, they used that chart and found that z0.025 = 1.96. I just don't see this though. If you look up 0.025 in the chart, you get 0.1985. In fact, all the values in the chart are decimals, so how did they get 1.96?

2. Dec 16, 2009

Staff: Mentor

The table is one of probabilities P(0 <= z <= n.nn), where n.n is one of the numbers down the left column and 0.0n is a number across the top row.

z0.025 is the z score for which the probability that z > some number is 0.025. Another way to say this is that the probability (or area) in the "tail" is 0.025. This means that the remaining probability is 0.975. Since the table gives probabilities for z values that are greater than or equal to 0, the probability you want is 0.475.

Look in the body of the table for 0.475. You will find this in the row that is marked 1.9, and in the column marked 0.06. What this is telling you is that P(0 <= z <= 1.96) = 0.475, or equivalently, P(z > 1.96) = 0.025.

3. Dec 17, 2009

60051

How did you get 0.475? 0.95/2?

4. Dec 17, 2009

Staff: Mentor

That will work, but you can also subtract .025 from .500.

5. Dec 17, 2009

HallsofIvy

??They rounded off to two decimal places!

6. Dec 17, 2009

Staff: Mentor

HoI, I think you missed that decimal point. If you round 0.1985 to two decimal places, you 0.20, not 1.96. My explanation is in post 2.

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