To determine which average height is most likely closest to the true average height of the population, we can analyze the given average heights of the four samples taken from the population of students.
We have the following sample sizes and their corresponding average heights:
1. Sample size: [tex]\(10\)[/tex], Average height: [tex]\(66\)[/tex] inches
2. Sample size: [tex]\(20\)[/tex], Average height: [tex]\(57\)[/tex] inches
3. Sample size: [tex]\(30\)[/tex], Average height: [tex]\(60\)[/tex] inches
4. Sample size: [tex]\(40\)[/tex], Average height: [tex]\(62\)[/tex] inches
Larger sample sizes typically provide a more accurate estimate of the population parameter because they reduce the margin of error. In this case, the sample with the largest size is [tex]\(40\)[/tex], where the average height is [tex]\(62\)[/tex] inches.
Therefore, the average height of [tex]\(62\)[/tex] inches, obtained from the largest sample size of [tex]\(40\)[/tex] students, is most likely the closest to the true average height of the entire population.
Hence, the correct answer is:
C. [tex]\(62\)[/tex]
