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

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

Two independent surveys asked random samples of 500 people about the distances they commute to work each day. The results of the surveys are detailed in the table below.

SurveyMean (miles)Standard deviation (miles)
A13.91.5
B15.11.5

Which statement is true based on the results of these surveys?

  1. There is a greater variation in the distribution of the distances people commute to work in Survey A.
  2. There is a greater variation in the distribution of the distances people commute to work in Survey B.
  3. The variation in the distribution of the distances people commute is the same in both surveys.
  4. It is impossible to determine the variation in the distribution of the distances people commute because the means are different.
▶️ Answer/Explanation
Solution

Answer: C

Both surveys have the same standard deviation of 1.5 miles, indicating equal variation.

Question Medium

A random sample of 400 town voters were asked if they plan to vote for Candidate A or Candidate B for mayor. The results were sorted by gender and are shown in the table below.

 Plan to vote for Candidate APlan to vote for Candidate B
Female20220
Male34144

The town has a total of 6,000 voters. Based on the table, what is the best estimate of the number of voters who plan to vote for Candidate A?

▶️ Answer/Explanation
Solution

Answer: 3540

Total voting for A in sample = 202 + 34 = 236. Estimate = \(\frac{236}{400} \times 6000 = 3540\).

Question   medium

A study conducted by a mobile phone company found that the average battery life of a random sample of its phones is 4.6 hours, with an associated margin of error of 0.5 hours. The study was then repeated with a much larger sample size, with the mean and margin of error of the new sample being calculated in the same way as the original study.

Which of the following is most likely true?

A) The margin of error from the new study is larger than the margin of error from the original study

B) The margin of error from the new study is smaller than the margin of error from the original study.

C) The mean from the new study is larger than the mean from the original study.

D) The mean from the new study is smaller than the mean from the original study

▶️Answer/Explanation

B) The margin of error from the new study is smaller than the margin of error from the original study.

The margin of error in a statistical study is influenced by the sample size. Generally, larger sample sizes result in smaller margins of error.

Given that the second study was conducted with a much larger sample size, it’s reasonable to assume that the margin of error from the new study is smaller than the margin of error from the original study.

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