The heights of a large population of students have a mean of 60" with a standard deviation of 3". What is the mean of the resulting distribution of sample means for n =16?
The mean would also be expected to be 60". Do you have specific scores to calculate the sample mean? This data was not included.
Well, if the mean height of the students is 60 inches, we can call them the "high risers". And if the standard deviation is 3 inches, we can say they have a tendency to "stand tall and proud".
Now, let's talk about the sample means. Since n = 16, it means we're looking at groups of 16 students at a time - let's call them the "squad".
The mean of the resulting distribution of sample means for n = 16 can be calculated by taking the mean of the original population, which is 60 inches, and dividing it by the square root of the sample size, which is √16.
So, the mean of the resulting distribution of sample means for n = 16 is 60 divided by 4, which is... 15 inches!
Now, that's what I call a "heightened" sense of humor!
The mean of the resulting distribution of sample means, also known as the "sampling distribution," can be calculated using the formula:
Mean of sampling distribution = Mean of population = 60 inches
Therefore, the mean of the resulting distribution of sample means for n = 16 is 60 inches.
To find the mean of the resulting distribution of sample means for n = 16, we can use the formula for the standard error of the mean.
The standard error of the mean (SE) is calculated by dividing the standard deviation (σ) of the population by the square root of the sample size (n).
SE = σ / √n
In this case, the standard deviation (σ) of the population is 3" and the sample size (n) is 16. Plugging these values into the formula, we get:
SE = 3 / √16
Simplifying, we have:
SE = 3 / 4
SE = 0.75
So, the standard error of the mean is 0.75.
Now, to find the mean of the resulting distribution of sample means, we can use the fact that the mean of all sample means will be equal to the mean of the population.
Given that the mean of the population is 60", we can conclude that the mean of the resulting distribution of sample means for n = 16 is also 60".
Therefore, the mean of the resulting distribution of sample means for n = 16 is 60".