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,	34,	33,	27,	28,	32,	31,	34,	32,	29
OF:	17,	14,	22,	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 μ₁for younger females and μ₂ for older females.)

H₀: μ₁ − μ₂ = 10
H_a: μ₁ − μ₂ < 10

H₀: μ₁ − μ₂ = 10
H_a: μ₁ − μ₂ > 10     

H₀: μ₁ − μ₂ = 0
H_a: μ₁ − μ₂ > 0

H₀: μ₁ − μ₂ = 0
H_a: μ₁ − μ₂ < 0

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	=

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 females.

Fail to reject H₀. The data suggests that true average lean angle for older females is more than 10 degrees smaller than that of younger females.    

Reject H₀. The data suggests that true average lean angle for older females is not more than 10 degrees smaller than that of younger females.

Reject H₀. The data suggests that true average lean angle for older females is more than 10 degrees smaller than that of younger females.

Answer 1

H₀: μ₁ − μ₂ = 10
H_a: μ₁ − μ₂ > 10

	Pop 1	Pop 2
sample mean x =	30.900	15.600
std deviation s=	2.514	4.037
sample size n=	10	5
std error se=s/√n=	0.795	1.806
degree freedom=(se12+se22)2/(se12/(n1-1)+se22/(n2-1))=			5

Point estimate =x1-x2=		15.300
standard error of difference Se=√(S21/n1+S22/n2)=			1.9729
test statistic t =(x1-x2-Δo)/Se=		2.686
p value : =	0.022		from excel: tdist(2.6864,5,1)

from above

t =2.69

p value =0.022

Reject H₀. The data suggests that true average lean angle for older females is more than 10 degrees smaller than that of younger females.