Random Sampling and Inferences Test Answer Key with Scoring – Grade 7

Question 1 Population and sample (2 points)

1. The population is all 400 regular customers.
2. The sample is the 60 customers who were asked.

Scoring: 1 point for each part.

Question 2 Random or biased (3 points)

1. Random: each student has an equal chance.
2. Biased: band members are not typical of all students and others are left out.
3. Biased: only students who read and choose to answer are included.

Scoring: 1 point per part for the correct label with a reason.

Question 3 Hiker survey (2 points)

27 ÷ 90 = 0.30. Estimate: 0.30 × 1,800 = 540.

About 540 hikers

Scoring: 1 point for the proportion, 1 point for the estimate.

Question 4 Pumpkin weights (3 points)

1. Sum = 110, so the mean is 110 ÷ 10 = 11 lb.
2. 350 × 11 = 3,850 lb.
3. Random picking gives every pumpkin a fair chance, so the sample is not tilted toward large or small pumpkins.

Scoring: 1 point for each part.

Question 5 Bike ownership samples (3 points)

1. 11 ÷ 20 = 55% and 15 ÷ 20 = 75%: 55% to 75%.
2. 13 ÷ 20 = 65%.
3. 0.65 × 900 = 585 students.

Scoring: 1 point for each part.

Question 6 Spot the bias (2 points)

Only listeners of that station can call, and only the people who choose to call are counted. Neither group is a random sample of the town.

The sample is biased because it includes only listeners who choose to call.

Scoring: 1 point for each valid reason.

Question 7 Combining samples (3 points)

1. 14 ÷ 40 = 35% and 24 ÷ 60 = 40%.
2. (14 + 24) ÷ (40 + 60) = 38 ÷ 100 = 38%.
3. 0.38 × 5,000 = 1,900 fish.

Scoring: 1 point for each part.

Question 8 Computer-drawn sample (2 points)

1. Yes, because every student on the roster has an equal chance of being chosen.
2. 12 ÷ 30 = 0.40 and 0.40 × 780 = 312 students.

Scoring: 1 point for each part.