Applied Mathematics · Class 12 Commerce
Ch 7Inferential Statistics — Class 12 Applied Mathematics, concept-first.
This concept map shows how the chapter fits together. Statistics splits into descriptive statistics — which summarises data and estimates the uncertainty in those summaries through the standard error — and inferential statistics, which uses a sample drawn from a population to draw conclusions about the whole.
Key concepts
Hover a concept to preview it and jump to its most relevant Q&A.
Degrees Of Freedom
Imagine you are standing in an empty room. You can walk forward and backward, slide left and right, and even jump up and down. That is three independent ways to change your position.
Most relevant Q&A
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Concept Map
This concept map shows how the chapter fits together. Statistics splits into descriptive statistics — which summarises data and estimates the uncertainty in those summaries through the standard error…
Introduction
Statistics is often used for more than describing a dataset — one of its most powerful applications is estimating the truth about an entire population from just a small sample of it.
Population and Sample
A population is the complete group of individuals or objects you want to draw conclusions about — every student enrolled in a school, every chip a factory produces in a week.
Parameter and Statistics and Statistical Interferences
Once a sample has been drawn, the next question is how to use it responsibly: what exactly are we measuring, and how much can we trust it? This section draws the line between a population-level parame…
Parameter and Statistics
A parameter is a numerical value describing the entire population — the population mean, for instance — computed from every single observation in it.
Statistical Significance and Sampling Distribution
A finding is called statistically significant when we're confident it's real — that it didn't arise from sampling error alone but reflects something genuinely true about the population, provided the s…
t-Test (a Test of Difference for Parametric Data)
Sometimes a decision requires more than describing a sample — it requires deciding whether an observed difference is real or just noise.
Hypothesis
To make a decision about a population, we first need something concrete to test — an assumption, which may turn out true or false, called a hypothesis.
+−Worked Examplesi2 questions
- Example 1If we want to examine that on an average college student take less than five years to complete their education. The null and alternative hyp…Free
- Example 2Consider a classroom having seating capacity of 30 students. The first 29 students have a choice to sit but the 30th student can only sit on…Preview
One Sample T- Test
The one-sample t-test checks whether a sample mean is genuinely different from a known or claimed population value.
T- Test for Two Independent Groups
The two-sample (independent-groups) t-test extends the same logic to comparing two groups against each other — an experimental group against a control group, say — to check whether their means differ…
Chapter Summary
This chapter built the logic of statistical inference — using the information in a sample to draw, and defend, conclusions about the whole population it came from — one of the core ideas of the CBSE C…
Exercise 5.1
+−5.17 questions
- Q1Identify the below statement as biased or Unbiased statement. Justify your answer. "For a survey about daily mobile uses by students, random…Free
- Q2(i) Find the critical $t$ value for $\alpha = 0.01$ with d.f. = 22 for a left-tailed test. (ii) Find the critical $t$ values for $\alpha = 0…Free
- Q3Suppose that a 95% confidence interval states that population mean is greater than 100 and less than 300. How would you interpret this state…Free
- Q4A shoe maker company produces a specific model of shoes having 15 months average lifetime. One of the employees in their R & D division clai…Preview
- Q5An electric light bulbs manufacturer claims that the average life of their bulb is 2000 hours. A random sample of bulbs is tested and the li…Preview
- Q6A fertilizer company packs the bags labelled 50 kg and claims that the mean mass of bags is 50 kg with a standard deviation 1kg. An inspecto…Preview
- Q7The average heart rate for Indians is 72 beats/minute. To lower their heart rate, a group of 25 people participated in an aerobics exercise…Preview
Worked Examples
Solved examples, worked out step by step.
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- Example 3For scheduling three hour-long tasks (read, eat and nap) between the hours of 5 p.m. and 8 p.m. we have two degrees of freedom as any two ta…Free
- Example 4Find the critical $t$ value for $\alpha = 0.05$ with d.f. = 16 for a right-tailed $t$ test.Free
- Example 5Let us consider the average rainfall in a given area is 8 inches. However, a local meteorologist claims that rainfall was above average from…Preview
- Example 6Country A has an average farm size of 191 acres, while Country B has an average farm size of 199 acres. Assume the data were attained from t…Preview