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Digital SAT Math : Inference from sample statistics and margin of error -Practice Questions

Digital SAT Math : Inference from sample statistics and margin of error -Practice Questions- New Syllabus

DSAT MAth Practice questions – all topics

  • Problem-solving and Data Analysis Weightage: 15%  Questions: 5-7
    • Ratios, rates, proportional relationships, and units
    • Percentages
    • One-variable data: distributions and measures of centre and spread
    • Two-variable data: models and scatterplots
    • Probability and conditional probability
    • Inference from sample statistics and margin of error
    • Evaluating statistical claims: observational studies and Experiments

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DSAT MAth and English  – full syllabus practice tests

Question Easy

A city has 50 city council members. A reporter polled a random sample of 20 city council members and found that 6 of those polled supported a specific bill. Based on the sample, which of the following is the best estimate of the number of city council members in the city who support the bill?

A) 6

B) 9

C) 15

D) 30

▶️ Answer/Explanation
Solution

Ans: C

Sample proportion: \( \frac{6}{20} = 0.3 \).

Estimated total: \( 0.3 \times 50 = 15 \).

Question Easy

A state representative wants to increase the amount of driving practice time required before a student can earn a driver’s license. The representative surveyed a random sample of 50 from the 250 students taking the driver’s education class at Jefferson High School.

The survey reported that 62% of students taking the class agree that driving practice time should be increased, with an associated margin of error of 5%.

Based on the results of the survey, how many of the students surveyed agree with the proposed change?

A) 19

B) 31

C) 124

D) 155

▶️ Answer/Explanation
Solution

Ans: B

Sample size: 50 students.

Percentage agreeing: 62%.

Number agreeing: \( 0.62 \times 50 = 31 \).

Question Easy

A certain forest is 253 acres. To estimate the number of trees in the forest, a ranger randomly selects 5 different 1-acre parcels in the forest and determines the number of trees in each parcel. The numbers of trees in the sample acres are 51, 59, 45, 52, and 73. Based on the mean of the sample, which of the following ranges contains the best estimate for the number of trees in the entire forest?

A) 11,000 to 12,000

B) 12,5600 to 13,500

C) 13,500 to 14,500

D) 18,000 to 19,000

▶️ Answer/Explanation
Solution

Ans: C

Mean trees per acre: \( \frac{51 + 59 + 45 + 52 + 73}{5} = 56 \).

Total estimate: \( 56 \times 253 = 14,168 \).

Range: 13,500 to 14,500 contains 14,168.

Question Easy

A city with 120,000 residents is voting on a proposal that would eliminate overnight parking of vehicles on the city’s streets. An independent company randomly surveys 1,200 residents to see whether or not residents would support this proposal. The outcome of the survey shows that 60% of the residents surveyed approve of the proposal with a margin of error of 2%. Which of the following statements is a plausible conclusion from the outcome of the survey?

A) Exactly 60% of city residents approve eliminating overnight parking.

B) There are 72,000 city residents who approve eliminating overnight parking.

C) About 2% of the city residents do not approve eliminating overnight parking.

D) Between 58% and 62% of the city residents approve eliminating overnight parking.

▶️ Answer/Explanation
Solution

Ans: D

Survey result: 60% approve, margin of error: 2%.

Range: \( 60 – 2 = 58\% \) to \( 60 + 2 = 62\% \).

Choice A: Incorrect, ignores margin of error.

Choice B: Incorrect, assumes exact percentage.

Choice C: Incorrect, misinterprets margin of error.

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