sample was obtained from a population with unknown parameters. scores: 6, 12, 0, 3, 4
compute the sample mean and sandard deviation. compute the estimated standard error for M.
Find the mean first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
SEm = SD/√(n-1)
I'll let you do the calculations.
To calculate the sample mean, you need to sum up all the scores in the sample and divide it by the total number of scores:
Sample Mean (M) = (6 + 12 + 0 + 3 + 4) / 5 = 25 / 5 = 5
The sample mean is 5.
To calculate the sample standard deviation, you need to follow these steps:
1. Calculate the difference between each score and the sample mean.
(6 - 5) = 1
(12 - 5) = 7
(0 - 5) = -5
(3 - 5) = -2
(4 - 5) = -1
2. Square each of these differences.
1^2 = 1
7^2 = 49
(-5)^2 = 25
(-2)^2 = 4
(-1)^2 = 1
3. Sum up all the squared differences.
1 + 49 + 25 + 4 + 1 = 80
4. Divide the sum of squared differences by (n-1), where n is the sample size.
80 / (5-1) = 80 / 4 = 20
5. Take the square root of the result.
√20 ≈ 4.47
The sample standard deviation is approximately 4.47.
To calculate the estimated standard error for M, you can divide the sample standard deviation by the square root of the sample size:
Estimated Standard Error for M = Sample Standard Deviation / √(Sample Size)
In this case, the sample size is 5.
Estimated Standard Error for M = 4.47 / √5 ≈ 1.99
To calculate the sample mean, you need to find the average of the given scores. Here are the steps:
1. Add all the scores together: 6 + 12 + 0 + 3 + 4 = 25.
2. Divide the sum by the number of scores (n). In this case, we have 5 scores, so divide 25 by 5: 25 / 5 = 5.
Therefore, the sample mean is 5.
To calculate the standard deviation, you can use the following steps:
1. Calculate the deviation of each score from the sample mean. To do this, subtract the mean (5) from each score. The deviations are: 6-5=1, 12-5=7, 0-5=-5, 3-5=-2, 4-5=-1.
2. Square each deviation: 1^2 = 1, 7^2 = 49, (-5)^2 = 25, (-2)^2 = 4, (-1)^2 = 1.
3. Calculate the sum of the squared deviations: 1 + 49 + 25 + 4 + 1 = 80.
4. Divide the sum by the number of scores minus 1 (n-1). In this case, we have 5 scores, so divide 80 by 4: 80/4 = 20.
5. Take the square root of the result. The square root of 20 is approximately 4.47.
Therefore, the standard deviation is approximately 4.47.
To compute the estimated standard error for the sample mean (M), you can use the following formula:
Estimated standard error (SE) = Standard deviation (s) / √(n), where n is the number of scores in the sample.
In this case, the standard deviation (s) is 4.47 and the number of scores (n) is 5. Plug these values into the formula:
SE = 4.47 / √(5) ≈ 2.00
Therefore, the estimated standard error for the sample mean is approximately 2.00.