Using the z-score of ±1.645 for the 5 percent cutoff and the z-score of ±1.96 for the 2.5 percent in the tail, identify the subject identification (ID) number for subjects who are closest to the cutoff for the upper 2.5 percent and 5 percent of the scores and the lower 2.5 percent and 5 percent of the scores.

Question

Using the z-score of ±1.645 for the 5 percent cutoff and the z-score of ±1.96 for the 2.5 percent in the tail, identify the subject identification (ID) number for subjects who are closest to the cutoff for the upper 2.5 percent and 5 percent of the scores and the lower 2.5 percent and 5 percent of the scores.

I am working on a project with ages and heights. I have the z-scores for both. I just don't understand the above question and how I am to find the upper and lower of the scores. Thank you, Lisa

Answer 1

Z = (score-mean)/SD

Insert Z, mean and SD values to solve for scores

Answer 2

To find the subject identification (ID) numbers for the upper and lower cutoffs based on z-scores, you first need to understand the concept of z-scores and their relationship to normal distribution.

A z-score represents the number of standard deviations a given value is from the mean of a distribution. It allows us to compare values from different distributions by transforming them to a standard normal distribution, where the mean is 0 and the standard deviation is 1.

In this case, you have z-scores of ±1.645 for the 5% cutoff and ±1.96 for the 2.5% cutoff in the tail. The cutoffs correspond to the percentiles of the standard normal distribution. To find the subject ID numbers for these cutoffs, you need to reverse-transform the z-scores back to their original values by using the mean and standard deviation of your data.

Here are the step-by-step instructions to find the subject ID numbers for the upper and lower cutoffs:

1. Calculate the mean (μ) and standard deviation (σ) of your data (ages or heights).

2. Multiply the z-scores by the standard deviation and add the mean to get the original values.

For the upper cutoff:
Upper cutoff value = z-score * standard deviation + mean

For the lower cutoff:
Lower cutoff value = z-score * standard deviation + mean

3. Identify the subject ID numbers that correspond to the upper and lower cutoff values you obtained.

For example, let's say you have age data and you calculated a mean of 40 and a standard deviation of 5. Using the given z-scores:

Upper cutoff value = 1.645 * 5 + 40 = 48.225
Lower cutoff value = -1.645 * 5 + 40 = 31.775

These values represent the age at which subjects would be closest to the upper 5% and lower 5% cutoffs, respectively.

Now, based on your own data and the z-scores provided, you can perform the calculations to find the subject ID numbers for the upper and lower cutoffs.