Question

As the population ages, there is increasing concern about accident-related injuries to the elderly. An article reported on an experiment in which the maximum lean angle—the furthest a subject is able to lean and still recover in one step—was determined for both a sample of younger females (21–29 years) and a sample of older females (67–81 years). The following observations are consistent with summary data given in the article:

YF:	28,	35,	31,	27,	28,	32,	31,	35,	32,	25
OF:	19,	14,	21,	13,	12

Carry out a test at significance level 0.10 to see whether the population standard deviations for the two age groups are different (normal probability plots support the necessary normality assumption).
State the relevant hypotheses. (Use σ₁ for YF and σ₂ for OF.)

H₀: σ₁ = σ₂

H_a: σ₁ ≤ σ₂

H₀: σ₁ = σ₂

H_a: σ₁ > σ₂

    

H₀: σ₁ = σ₂

H_a: σ₁ < σ₂

H₀: σ₁ = σ₂

H_a: σ₁ ≠ σ₂

Calculate the test statistic. (Round your answer to two decimal places.)
f =

What can be said about the P-value for the test?

P-value > 0.100

0.050 < P-value < 0.100   

0.010 < P-value < 0.050

0.001 < P-value < 0.010

P-value < 0.001

State the conclusion in the problem context.

Reject H₀. The data suggests that there is a difference between the two standard deviations.

Reject H₀. The data does not suggest that there is a difference between the two standard deviations.  

Fail to reject H₀. The data suggests that there is a difference between the two standard deviations.

Fail to reject H₀. The data does not suggest that there is a difference between the two standard deviations.

Answer 1

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