As the population ages, there is increasing concern about accident-related injur
ID: 3232106 • Letter: A
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: 29, 36, 31, 27, 28, 32, 31 35, 32, 27 OF: 18, 16, 22, 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 sigma_1 for YF and sigma_2 for OF) H_0: sigma_1 = sigma_2 H_a: sigma_1 lessthanorequalto H_a: sigma_2 H_0: sigma_1 = sigma_2 H_a: sigma_1 > sigma_2 H_0: sigma_1 = sigma_2 H_a: sigma_1 notequalto sigma_2 H_0: sigma_1 = sigma_2 H_a: sigma_1Explanation / Answer
From following output test statistic F=0.60 and p-value=0.482
Test and CI for Two Variances: YF, OF
Method
Null hypothesis (YF) / (OF) = 1
Alternative hypothesis (YF) / (OF) 1
Significance level = 0.05
F method was used. This method is accurate for normal data only.
Statistics
95% CI for
Variable N StDev Variance StDevs
YF 10 3.120 9.733 (2.146, 5.696)
OF 5 4.025 16.200 (2.411, 11.566)
Ratio of standard deviations = 0.775
Ratio of variances = 0.601
95% Confidence Intervals
CI for
CI for StDev Variance
Method Ratio Ratio
F (0.260, 1.684) (0.067, 2.835)
Tests
Test
Method DF1 DF2 Statistic P-Value
F 9 4 0.60 0.482
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