Question

According to the U.S. Department of Education. Institute of Education Sciences, National Center for Education Statistics 1,026,000 high school seniors (rounded to the nearest thousand) took the ACT test as part of the college admissions process. The mean composite score was 21.1 with a standard deviation of 4.8. The ACT composite score ranges from 1 to 36, with higher scores indicating greater achievement in high school.

According to the central limit theorem, what are the mean and standard error of the distribution of sample means for a sample of 50 students?

a. 50 and 21.1

b. 21.1 and 4.8

c. 21.1 and 0.68

d. 21.1 and 0.10

Answer 1

The correct option is C) 21.1 and 0.68

Explanation:

Consider the provided information.

The mean composite score was 21.1 with a standard deviation of 4.8. The ACT composite score ranges from 1 to 36, with higher scores indicating greater achievement in high school.

Therefore μ = 21.1 and σ = 4.8

It is given that the sample of 50 students;

Thus, sample size ( n ) = 50

According to the central limit theorem,

`\mu_(\bar x)=\mu\ and \ \sigma_(\bar x)=(\sigma)/(√(n))`

Therefore

`\mu_(\bar x)=21.1`

`\sigma_(\bar x)=(4.8)/(√(50))`

`\sigma_(\bar x)=0.68`

Hence, the correct option is C) 21.1 and 0.68