Sample Z-Score and Standard ErrorSuppose the population has a mean of 350 and a standard deviation of 90, and you get a sample mean of 370.16 for a sample size of 36, what will be the sample z-score?9.721.34153.83
Question
Sample Z-Score and Standard ErrorSuppose the population has a mean of 350 and a standard deviation of 90, and you get a sample mean of 370.16 for a sample size of 36, what will be the sample z-score?9.721.34153.83
Solution
To calculate the sample z-score, you can use the formula:
Z = (X - μ) / (σ/√n)
where:
- X is the sample mean
- μ is the population mean
- σ is the standard deviation of the population
- n is the sample size
Given:
- X = 370.16
- μ = 350
- σ = 90
- n = 36
Substitute these values into the formula:
Z = (370.16 - 350) / (90/√36)
Simplify the denominator:
Z = (370.16 - 350) / (90/6)
Subtract the means:
Z = 20.16 / 15
Finally, divide to find the z-score:
Z = 1.34
So, the sample z-score is 1.34.
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