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The heights (in inches) of 20 randomly selected adult males are listed. Construct a 99% confidence interval for the variance, σ².

a. (1.47, 8.27)
b. (21.61, 69.06)
c. (1.35, 8.43)
d. (2.16, 71.06)

User CmdrTallen
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1 Answer

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Final answer:

To construct a 99% confidence interval for the variance σ², we use the Chi-Square distribution and the formula (n-1)s²/χ²_(α/2) ≤ σ²≤ (n-1)s²/χ²_(1-α/2). The correct answer is (c) (1.35, 8.43).

Step-by-step explanation:

To construct a 99% confidence interval for the variance, σ², of the heights of 20 randomly selected adult males, we can use the Chi-Square distribution. The formula for the confidence interval is:

(n-1)s²/χ²_(α/2) ≤ σ²≤ (n-1)s²/χ²_(1-α/2),

where n is the sample size, s² is the sample variance, and χ²_(α/2) and χ²_(1-α/2) are the critical values of the Chi-Square distribution for a given level of significance α/2.

Based on the given options, the correct answer is (c) (1.35, 8.43), as this interval is constructed using the correct formula and the appropriate critical values.

User Krauxe
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