A sample of n = 9 scores is obtained from a population with ƒÝ = 70 and ƒã = 18. If the sample mean is M = 76, then what is the z-score for the sample mean?
a. z = 0.33
b. z = 0.50
c. z = 1.00
d. z = 3.00
Formula:
z = (x - mean)/(sd/√n)
With your data:
z = (76 - 70)/(18/√9) = 6/6 = 1
Choice: c
Thank you for the help.
To find the z-score for the sample mean, we can use the formula:
z = (M - µ) / (σ / √n)
where M is the sample mean, µ is the population mean, σ is the population standard deviation, and n is the sample size.
From the given information:
M = 76 (sample mean)
µ = 70 (population mean)
σ = 18 (population standard deviation)
n = 9 (sample size)
Now we can substitute these values into the formula:
z = (76 - 70) / (18 / √9)
z = 6 / (18 / 3)
z = 6 / 6
z = 1
Therefore, the z-score for the sample mean is 1.
The correct answer is c. z = 1.00
To find the z-score for the sample mean, you can use the formula:
z = (X - ƒÝ) / (ƒã / √n)
where:
- X is the sample mean
- ƒÝ is the population mean
- ċ is the population standard deviation
- n is the sample size
In this case, X = 76, ƒÝ = 70, ƒã = 18, and n = 9. Plugging in these values into the formula, we get:
z = (76 - 70) / (18 / √9)
z = 6 / (18 / 3)
z = 6 / 6
z = 1
Therefore, the z-score for the sample mean is 1, which corresponds to option c.