Using Random Samples to Make Inferences About Populations(TEKS.Math.7.6.F)
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Texas 7th Grade Math › Using Random Samples to Make Inferences About Populations(TEKS.Math.7.6.F)
A random sample of 80 teenagers shows 32 prefer streaming music. The city has 50,000 teenagers. How many in the whole population likely prefer streaming?
20000
16000
32000
50000
Explanation
Use the sample proportion: $32/80 = 0.40$. Scale to the population: $0.40 \times 50{,}000 = 20{,}000$. Because this is based on a random sample, it is an estimate and the actual number may differ slightly.
Quality control tests a random sample of 100 items and finds 3 defective. The company produces 10,000 items in a day. What can you infer about the population of items produced that day?
30 defective
300 defective
3,000 defective
10 defective
Explanation
Sample defect rate: $3/100 = 0.03$ (3%). Estimated defects: $0.03 \times 10{,}000 = 300$. This is an estimate from a random sample; the true number may vary.
A library surveys a random sample of 150 students; 45 say they checked out a book this month. The school has 1,200 students. How many students in the whole school likely checked out a book this month?
150
540
360
45
Explanation
Proportion from sample: $45/150 = 0.30$. Apply to population: $0.30 \times 1{,}200 = 360$. Since this comes from a random sample, it is an estimate and may not be exact.
In a random sample of 200 households in a city, 18 have a vegetable garden. The city has 62,000 households. What can you infer about the number of households with gardens in the city?
1800
6200
558
5580
Explanation
Estimate the proportion: $18/200 = 0.09$. Scale up: $0.09 \times 62{,}000 = 5{,}580$. This is an estimate from a random sample; the actual number could be a bit different.
A middle school polls a random sample of 250 students; 85 want school buses to arrive earlier. The district has 4,000 students. How many in the whole population likely prefer earlier buses?
1360
850
1020
3400
Explanation
Sample proportion: $85/250 = 0.34$. Population estimate: $0.34 \times 4{,}000 = 1{,}360$. Because this uses a random sample, it is an estimate with some uncertainty.