Final answer:
The estimated population proportion of students with mathematics scores below grade level in the school district is approximately 33.2%, calculated by dividing 164 by 494.
Step-by-step explanation:
To estimate the population proportion based on a sample statistic, we can use the sample proportion as an estimate for the population proportion. In this case, out of a sample of 494 students, 164 have mathematics scores below grade level. To calculate the sample proportion, we divide the number of students with scores below grade level by the total number of students sampled:
Sample proportion = Number of students below grade level / Total number of students sampled = 164 / 494
Thus, the estimated population proportion is:
Estimated population proportion = 164 / 494 ≈ 0.332 (rounded to three decimal places)
This indicates that approximately 33.2% of the students in the entire school district are estimated to have mathematics scores below grade level, based on this sample.