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 anglethe farthest 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, 36, 31, 27, 28, 32, 31, 36, 32, 26 OF: 17, 15, 23, 13, 12 Does the data suggest that true average maximum lean angle for older females (OF) is more than 10 degrees smaller than it is for younger females (YF)? State and test the relevant hypotheses at significance level 0.10. (Use ul for younger females and up for older females.) O Ho: Mi - M2 = 0 Ha: Uli - U2 > 0 O Ho: U1 - 42 = 0 Ha: Mi - U2 < 0 Ho: U1 - U2 = 10 Ha: Mi - M2 > 10 O Ho: 41 - 42 = 10 Ha: M1 - M2 < 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.) t = P-value =

Answer 1

YF	OF
30.70	16.00	mean
3.50	4.36	std. dev.
10	5	n

Test Statistic :-
t = (X̅1 - X̅2) / SP √ ( ( 1 / n1) + (1 / n2))

Sp=(V(n1 – 1)S? + (n2 – 1)53)/(n1+ n2 – 2)

Sp = 3.784

t = 2.27

P value = P ( t > 2.27 ) = 0.021