Question

1. a random sample of 112 students at newton county middle school was surveyed about their favorite class. of those 112 students, 16 chose social studies class and 52 chose language arts. select a number from each dropdown menu to make the following sentence true. based on this sample survey, it is likely that choice 1 of the 560 students who attended newton county middle school would choose social studies as their favorite class, and choice 2 students would choose language arts as their favorite class. choice 1: 48, 32, 80, 112; choice 2: 32, 112, 144, 260

Explanation:

Step1: Calculate proportion for social - studies

Find the proportion of students who chose social - studies in the sample. The proportion $p_1$ in the sample of $n = 112$ students is $\frac{16}{112}=\frac{1}{7}$.

Step2: Estimate number for social - studies

Multiply the proportion by the total number of students. For the total of $N = 560$ students, the estimated number of students who choose social - studies is $560\times\frac{1}{7}=80$.

Step3: Calculate proportion for language - arts

Find the proportion of students who chose language - arts in the sample. The proportion $p_2$ in the sample of $n = 112$ students is $\frac{52}{112}=\frac{13}{28}$.

Step4: Estimate number for language - arts

Multiply the proportion by the total number of students. For the total of $N = 560$ students, the estimated number of students who choose language - arts is $560\times\frac{13}{28}=260$.

Answer:

Choice 1. 80
Choice 2. 260