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In: Statistics and Probability

Which z-score formula to use for the question below? z = x - mean / sd...

Which z-score formula to use for the question below?

z = x - mean / sd

or z = x - population mean / (sd /sqrt(n))

member_ID	TotalScore
1	26
2	29
3	31
4	23

1. Assume sample mean = 7.1 and SD = 3.19, calculate the z-score of each members based on sample mean and SD.

2. Given that population mean = 9.1 and SD = 4.2, calculate the z-score of each members based on the population mean and SD.

Expert Solution

If we are to determine how far each score is from its mean (sample / population), we need to go for Z score for individual observations 'x'; the formula is given by,

......................(for sample mean and sample SD)

......................(for population mean and population SD)

Here, we have to find the Z scores for these individual values:

1. For

Member 1:

Member 2:

Member 3:

Member 4:

2. For

Member 1:

Member 2:

Member 3:

Member 4:

However, if we are to determine how far a sample mean score is from its population mean, then Score changes to means score () and since the standard error of mean is SD / , SD changes to SE ().The Z score would then be defined as:

Suppose, we were to determine the Z score of the sample mean, where, (say), then,

orchestra answered 3 years ago

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