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 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, 36, 32, 26 OF: 18, 14, 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 A for younger females and 2 for older females.) Hai 1-2 > 0 Hai 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.) P-value= 0.510 State the conclusion in the problem context. t= 2.03 Fail to 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. Fail to reject Ho-The data 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. Reject Ho. The data suggests that true average lean angle for older females is more than 10 degrees smaller than that of younger females.

Explanation / Answer

Given that,

mean(x)=30.8

standard deviation , s.d1=3.4254

number(n1)=10

y(mean)=16

standard deviation, s.d2 =4.5277

number(n2)=5

null, Ho: u1 - u2 = 10

alternate, H1: u1 - u2 > 10

level of significance, = 0.1

from standard normal table,right tailed t /2 =1.533

since our test is right-tailed

reject Ho, if to > 1.533

we use test statistic (t) = (x-y)- U /sqrt(s.d1^2/n1)+(s.d2^2/n2)

to =((30.8-16) - 10 )/sqrt((11.73337/10)+(20.50007/5))

to =2.0902

| to | =2.0902

critical value

the value of |t | with min (n1-1, n2-1) i.e 4 d.f is 1.533

we got |to| = 2.09023 & | t | = 1.533

make decision

hence value of | to | > | t | and here we reject Ho

p-value:right tail - Ha : ( p > 2.0902 ) = 0.00149

ANSWERS

---------------

null, Ho: u1 = u2

alternate, H1: u1 > u2

test statistic: 2.0902

critical value: 1.533

decision: reject Ho

p-value: 0.00149

Option D

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