Inferential Statistics — Practice Quiz
CBSE · Class 12 · Applied Mathematics
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Quick Quiz: Inferential Statistics
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A sample of 25 students has a mean height of 165 cm and standard deviation of 8 cm. What is the standard error of the mean?
For a sample size of 20, what are the degrees of freedom for a one-sample t-test?
If the population mean is 50 and a sample mean is 52 with standard error 1.5, calculate the sampling error.
For a one-sample t-test with sample mean = 75, population mean = 70, sample standard deviation = 12, and n = 16, calculate the t-statistic.
Sample Questions
Which of the following are characteristics of a representative sample? (Select all correct answers)
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Contains random selection component, Large enough to show population variability, Accurately reflects population characteristics
A representative sample must have random selection, adequate size for variability, and reflect population characteristics. It's smaller than population and doesn't use convenience sampling.
A factory claims average production time is 45 minutes. A sample of 9 items shows mean time of 48 minutes with standard deviation 6 minutes. Calculate the t-statistic for testing this claim.
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1.5
t = (x̄ - μ₀)/(s/√n) = (48 - 45)/(6/√9) = 3/(6/3) = 3/2 = 1.5. Common mistake: Not calculating standard error correctly.
In systematic random sampling, if population size is 120 and sample size needed is 12, what is the sampling interval?
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10
Sampling interval = Population size / Sample size = 120/12 = 10. This means every 10th item is selected. Common mistake: Confusing this with sample size itself.
If two samples have means 32 and 28, with pooled standard deviation 4 and sample sizes 16 and 25 respectively, calculate the t-statistic for comparing means.
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3.125
t = (x̄₁ - x̄₂)/(Sp√(1/n₁ + 1/n₂)) = (32-28)/(4√(1/16 + 1/25)) = 4/(4√(0.0625+0.04)) = 4/(4√0.1025) = 4/(4×0.32) = 4/1.28 = 3.125
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Sources & Official References
- NCERT Official — ncert.nic.in
- CBSE Academic — cbseacademic.nic.in
- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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