A sociologist surveyed a random sample of students at a high school about their primary mode of transportation to schoo…

The correct answer is 180. To find the best estimate, we first need to determine the total size of the sample. Summing all the values in the table gives the total number of students surveyed:

(15 + 40 + 10) + (30 + 35 + 5) + (45 + 10 + 5) + (45 + 5 + 5) = 65 + 70 + 60 + 55 = 250 students.

Next, we find the proportion of 11th-grade students who travel by car in the sample. The table shows this is 45 out of 250 students, or 45/250.

We can use this proportion to estimate the number of such students in the entire school of 1,500: (45/250) · 1,500 = 270 students.

Then, we find the proportion of 9th-grade students who travel by car in the sample. The table shows this is 15 out of 250 students, or 15/250.

We estimate the number of such students in the entire school: (15/250) · 1,500 = 90 students.

Finally, the question asks how much greater the estimated number of 11th-grade car travelers is than the 9th-grade car travelers. We find the difference: 270 - 90 = 180.

Alternatively, one could find the difference in the sample (45 - 15 = 30) and then scale this difference up to the population. The scaling factor is the total school population divided by the total sample population, which is 1,500 / 250 = 6. The estimated difference is 30 · 6 = 180.

A is incorrect because it is the difference in the sample counts (45 - 15 = 30) without scaling up to the full school population.

B is incorrect because it results from comparing the wrong grades, likely 11th grade (45) and 10th grade (30). The difference in the sample is 15, which when scaled to the population gives 15(1500/250) = 90.

D is incorrect because it results from incorrectly assuming the sample size is 100. Finding the sample difference (30) and scaling it by a factor of 1500/100 = 15 gives 30 · 15 = 450.