Question

Suppose 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. The standard error of the mean for this sample is

A) 10.6
B) 9.1
C) 63.7
D) 28.4

Answer 1

The standard error of the mean for this sample is 9.1.

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
`\pm` Margin of error

where, Sample mean =
`\bar X` = 490.4

Margin of error =
`Z_(\alpha)/(2) * (\sigma)/(√(n) )`

Here,
`\sigma` = standard deviation = 63.7

n = sample of students = 49

So, Standard error formula is given by =
`(\sigma)/(√(n) )`

=
`(63.7)/(√(49) )` = 9.1

Therefore, standard error of the mean for this sample is 9.1.