Consider a population with mean = 43 and sd = 5.2. Calculate the x-score for an sample mean of 46.5 from a sample of size 35.
Do you mean Z score?
Z = (sample mean - pop. mean)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√(n-1)
If only one SD is provided, you can use just that to determine SEdiff.
mean = 5.2 sd= 1.6 find standard deviation of sample
To calculate the z-score, also known as the standard score, for a sample mean, we need to use the formula:
z = (x - μ) / (σ / √n)
Where:
- z is the z-score
- x is the sample mean
- μ is the population mean
- σ is the population standard deviation
- n is the sample size
In this case, the population mean (μ) is 43, the population standard deviation (σ) is 5.2, the sample mean (x) is 46.5, and the sample size (n) is 35.
Now let's substitute the values into the formula:
z = (46.5 - 43) / (5.2 / √35)
First, let's calculate the value inside the square root:
√35 ≈ 5.92
Now let's substitute it into the formula:
z = (46.5 - 43) / (5.2 / 5.92)
Calculate the division:
z = 3.5 / 0.88
Perform the division to find the z-score:
z ≈ 3.98
So, the z-score for a sample mean of 46.5 from a sample of size 35 is approximately 3.98.