Final answer:
The sample size (n) is approximately calculated as 2 when using the formula SE(y) = s / √n with the provided standard error and standard deviation. However, this result is practically improbable and suggests a potential error in the question.
Step-by-step explanation:
To calculate the sample size (n) used when given the standard error (SE(y)) and the sample standard deviation (s), you can use the following formula relating these quantities:
SE(y) = s / √n
Plugging in the given values, we have:
2.673 = 4.01 / √n
Squaring both sides to remove the square root gives:
(2.673)^2 = (4.01)^2 / n
7.145129 = 16.0801 / n
We can now solve for n by dividing both sides by 7.145129:
n = 16.0801 / 7.145129
n = 2.2512
Since the sample size must be a whole number, we round to the nearest whole number. Therefore, the approximate sample size used is 2.
It is important to note that this result seems incorrect because, in practice, we would expect a sample size much larger than 2, especially when dealing with standard deviations and standard errors. There may have been a misunderstanding or typographical error in the original question provided by the student.