As the population ages, there is increasing concern about accident-related injur

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 farthest 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: subject is able to lean and still recover in one step-was determined for bath YF: 29, 36, 32, 27, 28, 32, 31, 35, 32, 27 OF: 17, 15, 22, 13, 12 Does the data suggest that true average maximum older females. ean angle for older ema es OF is more than 10 degrees smaller than it is or younger females YF)? State and test the elevant hypotheses at significance a 0.10. Use#1 or younger females and ?2 for @ Ho: ?! _ ?2-0 Ha: ?1-?2 > 10 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) .value- State the conclusion in the problem context Fail to reject H0. The data suggests that true average lean angle for older females is not more than 10 degrees smaller than that of younger remales Fail to raject Ho. The data suggests that true average lean angle for older females is more than 10 degrees smaler than that of younger females. O Reject Ho. The deta suggests that true average lean angle for older females is more than 10 degrees smaller than that of younger females Reject Ho. The data suggests that true average lean angle for older females is not more than 10 degrees smaller than that of younger females

Explanation / Answer

H0 : mu1 - mu2 = 10
Ha : mu1 - mu2 > 10

t = (x1 -x2 - 10)/sqrt(s1^2/n1 +s2^2/n2)
= (30.90 - 15.8 - 10)/sqrt(3.9623^2/5 + 3.1429^2/10)
= 2.51

df = 5 - 1 = 4

p value = 0.0330

Correct answer is
Option C)

Given Data Sample 1 Sample 2 Name mean 30.9 15.8 Sample size 10 5 Std. dev. 3.1429 3.9623

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