Correlation and RegressionMCQPYQ Jun 23Question 3767 of 188
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Given that r=0.4\displaystyle r = 0.4 and n=81\displaystyle n = 81, determine the limits for the population correlation coefficient.

Options

A(0.333,0.466)\displaystyle (0.333, 0.466)
B(0.367,0.433)\displaystyle (0.367, 0.433)
C(0.337,0.463)\displaystyle (0.337, 0.463)
D(0.373,0.427)\displaystyle (0.373, 0.427)
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Correct Answer

✅ Option c — (0.337,0.463)\displaystyle (0.337, 0.463)

All Options:

  • A(0.333,0.466)\displaystyle (0.333, 0.466)
  • B(0.367,0.433)\displaystyle (0.367, 0.433)
  • C(0.337,0.463)\displaystyle (0.337, 0.463)
  • D(0.373,0.427)\displaystyle (0.373, 0.427)

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Detailed Solution & Explanation

We are given: - Sample correlation coefficient, r=0.4\displaystyle r = 0.4 - Number of observations, n=81\displaystyle n = 81 The Probable Error (P.E.\displaystyle P.E.) of the correlation coefficient is calculated using the formula: P.E.=0.6745timesfrac1−r2sqrtnP.E. = 0.6745 \\times \\frac{1 - r^2}{\\sqrt{n}} Substitute the given values into the formula: P.E.=0.6745timesfrac1−(0.4)2sqrt81P.E. = 0.6745 \\times \\frac{1 - (0.4)^2}{\\sqrt{81}} P.E.=0.6745timesfrac1−0.169P.E. = 0.6745 \\times \\frac{1 - 0.16}{9} P.E.=0.6745timesfrac0.849P.E. = 0.6745 \\times \\frac{0.84}{9} P.E.=0.6745times0.09333approx0.06295P.E. = 0.6745 \\times 0.09333 \\approx 0.06295 Rounding to three decimal places, we get: P.E.approx0.063P.E. \\approx 0.063 The limits for the population correlation coefficient are given by: textLimits=rpmP.E.\\text{Limits} = r \\pm P.E. textLowerLimit=0.4−0.063=0.337\\text{Lower Limit} = 0.4 - 0.063 = 0.337 textUpperLimit=0.4+0.063=0.463\\text{Upper Limit} = 0.4 + 0.063 = 0.463 Thus, the limits for the population correlation coefficient are (0.337,0.463)\displaystyle (0.337, 0.463). Hence, **Option C** is the correct answer.

About This Chapter: Correlation and Regression

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Correlation Coefficient, Regression Equations

This chapter covers Correlation Coefficient, Regression Equations and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

Key Concepts to Understand

Correlation

A statistical measure that expresses the extent to which two variables are linearly related.

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