Decoding Z-Score Chart Accuracy

[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 z_0.025 = 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?

 

[Mark44]

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.

z_0.025 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.

 

[60051]

How did you get 0.475? 0.95/2?

 

[Mark44]

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

 

[HallsofIvy]

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 z_0.025 = 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?

??They rounded off to two decimal places!

 

[Mark44]

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.