Scores on an SAT test have a mean of μ = 1026 and a standard deviation of σ = 209. Compute the margin of error of the sample mean for a random sample of 100 students.
What is the value of the sample mean?
Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√n
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
The margin of error (ME) is calculated using the formula:
ME = z * (σ / √n)
Where:
z is the z-score or the critical value of the desired confidence level.
σ is the standard deviation of the population.
√n is the square root of the sample size.
Since the sample size is 100, we can calculate the margin of error as follows:
ME = z * (σ / √n)
ME = z * (209 / √100)
To determine the value of z, we need to specify the desired confidence level. Let's assume a 95% confidence level, which corresponds to a z-value of approximately 1.96.
ME = 1.96 * (209 / 10)
ME ≈ 40.94
Therefore, the margin of error for a sample mean of 100 students is approximately 40.94.
To compute the margin of error for the sample mean, we need to use the formula:
Margin of Error = Z * (σ / √n)
Where:
Z is the Z-score for the desired confidence level,
σ is the standard deviation,
n is the sample size.
In this case, the sample size is 100, so n = 100. The standard deviation is σ = 209.
The Z-score depends on the desired confidence level. Let's assume we want a 95% confidence level, which corresponds to a Z-score of 1.96 (you can find this value in a standard normal distribution table).
Plugging in the values into the formula, we get:
Margin of Error = 1.96 * (209 / √100)
= 1.96 * (209 / 10)
= 1.96 * 20.9
≈ 40.93
Therefore, the margin of error for the sample mean for a random sample of 100 students is approximately 40.93.