Calculate Z Value for Norman Distribution

[wmnch]

Hi experts,

Could you please explain how this Z value calculated? Please see the attached data set.

I always get a different Z value for 95%.

 

[wmnch]

Also, would like to know what excel formulas can use to calculate.

 

[Dr.Peterson]

Could you please explain how this Z value calculated? Please see the attached data set.

I always get a different Z value for 95%.

Please show how you are doing it, and what you got instead of 1.65. We can't tell what you might be doing wrong without seeing your work. It sounds like you are supposed to use a table; they differ, so we may need to see your table.

 

[wmnch]

Please show how you are doing it, and what you got instead of 1.65. We can't tell what you might be doing wrong without seeing your work. It sounds like you are supposed to use a table; they differ, so we may need to see your table.

Thanks for the reply.

I used the below table and for 95% I picked 0.4750 as the area under the curve.




I followed below video,

 

[Dr.Peterson]

Thanks for the reply.

I used the below table and for 95% I picked 0.4750 as the area under the curve.

The video is doing something different from what you want. It is finding, as it says at the very start, the critical value $z_{\alpha/2}$, which is used for a confidence interval. You want, at least judging by the numbers they get, the value of z such that the area to the left is 0.95, not so that the area between 0 and z is half of 0.95.

The explanation for your problem is unclear as to what is supposed to equal 95%; "the value for z of 0.95" is very poorly stated.

I would imagine that what they mean has been explained previously. You have also omitted the problem itself, which should at least give a clue.

Can you show the problem?

 

[wmnch]

Hi,

This is the full question.
I am not sure how to use the table to get the 95% area under the normal distribution curve.

 

[Dr.Peterson]

Hi,

This is the full question.
I am not sure how to use the table to get the 95% area under the normal distribution curve.

View attachment 25403

This does clarify one thing: They explicitly emphasize they are using "single sided values of z", whereas the video you looked at was double-sided (a confidence interval, which concerns values bounded on both sides).

I'm a little baffled, however, by the statement that "the largest number in the matrix is 0.50", which is not true of anything you showed. Is "the matrix" something else that you omitted, or is the problem just wrong??

And they still don't clearly define what they mean by "the 95% value of the data set", which is not standard terminology in my experience (though I am not a statistician, so my experience is limited).

All I can do is to work backward from their answer, and think about what possibilities there are. To me, having mostly used a different kind of table that gives the area below a given z, rather than between 0 and z, the most natural interpretation is that that area is 0.95. Using your table, since the area to the left of zero is 0.50, we have to look up an area of 0.95 - 0.50 = 0.45. And where do we find that area?



Right between1.64 and 1.65, which average to 1.645. That appears to be what they are using.

You also asked about Excel. To do this, you would use =NORM.S.INV(0.95), which displays 1.644853627; note that your book's 1.648 is a typo for 1.6448!