Respuesta :
Answer:
The standard error of the mean for this sample is 9.1.
Step-by-step explanation:
We are given that the average math SAT score for students enrolled at local community college is 490.4 with a standard deviation of 63.7.
A random sample of 49 students has been selected.
Since we know that the confidence interval is created by the given formula;
Suppose we have to calculate 95% confidence interval;
So, 95% Confidence interval = Sample mean [tex]\pm[/tex] Margin of error
where, Sample mean = [tex]\bar X[/tex] = 490.4
Margin of error = [tex]Z_\frac{\alpha}{2} \times \frac{\sigma}{\sqrt{n} }[/tex]
Here, [tex]\sigma[/tex] = standard deviation = 63.7
n = sample of students = 49
So, Standard error formula is given by = [tex]\frac{\sigma}{\sqrt{n} }[/tex]
= [tex]\frac{63.7}{\sqrt{49} }[/tex] = 9.1
Therefore, standard error of the mean for this sample is 9.1.
