Part 1 : Ben takes a random sample of 25 students in his seventh-grade class and finds that 85% of the sample prefers math over science. There are 150 students in the seventh grade. Based on the sample proportion, about how many students in the seventh grade would be expected to prefer math over science?
Option 1 : 25
Option 2 : 85
Option 3 :150
Option 4 :128
Solutions - Convert the percent into decimal and multiply.
85% of 150 = 0.85 * 150
= 127.5 which is rounded to 128
Part 2 : Mark wants to know how many families in his neighborhood plan to attend the neighborhood party. He puts all 80 of the neighborhood addresses in a hat and draws a random sample of 20 addresses. He then asks those families if they plan to attend the party. He finds that 20% of the families plan to attend the party. He claims that 20% of the neighborhood families would be expected to attend the party. Is this a valid inference?
No, this is not a valid inference because he asked only 20 families
No, this is not a valid inference because he did not take a random sample of the neighborhood
Yes, this is a valid inference because he took a random sample of the neighborhood
Yes, this is a valid inference because the 20 families speak for the whole neighborhood
Solutions : Plans to attend doesn't mean they would come. It is a 50/50 chance. 2/8 * 100% is 25%.
Answer = (C) = Yes, this is a valid inference because he took a random sample of the neighborhood
