population with a mean of 53.1 and standard deviation of 4.43 Calculate z score for xbar 49.8 from a sample of size 11
Someone please please help me!
Z = (mean1 - mean2)/SEm
SEm = SD/√n
Sure, I'd be happy to help you with your question!
To calculate the z-score for a sample mean, you can use the formula:
z = (x - μ) / (σ/√n)
Where:
- x is the sample mean
- μ is the population mean
- σ is the population standard deviation
- n is the sample size
Given:
Sample mean (x) = 49.8
Population mean (μ) = 53.1
Population standard deviation (σ) = 4.43
Sample size (n) = 11
Now, let's calculate the z-score:
z = (49.8 - 53.1) / (4.43 / √11)
First, calculate the value inside the square root:
√11 ≈ 3.3166
Now, substitute the values into the formula:
z = (49.8 - 53.1) / (4.43 / 3.3166)
Simplify further:
z = -3.3
Therefore, the z-score for xbar 49.8 from a sample of size 11 is approximately -3.3.
Note: The negative sign indicates that the sample mean is below the population mean.