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:

Use the following R code to visualize the data, perform a t test and calculate the 95% CI.
#Data and R Code

YF = c(	29,	36,	33,	27,	28,	32,	31,	34,	32,	27,	28,	39,	29,	34,	33,	27,	28,	32,	31,	34)
OF = c(	25,	19,	21,	23,	22,	19,	15,	26,	17,	15,	23,	17)

boxplot(YF, OF)
t.test(YF, OF, alternative = "greater")
t.test(YF, OF)$conf.int

Which of the following is true based on the side by side boxplot of the data?

The older females tend to have higher maximum lean angles than younger females.The younger females tend to have higher maximum lean angles than older females.    The maximum lean angle is approximately the same for younger and older females.

Does the data suggest that true average maximum lean angle for younger females (YF) is more than it is for older females (OF)? State and test the relevant hypotheses at significance level 0.05 by obtaining a P-value. (Use μ₁ for younger females and μ₂ for older females.)

H₀: μ₁ − μ₂ = 0
H_a: μ₁ − μ₂ < 0H₀: x₁ − x₂ = 0
H_a: x₁ − x₂ < 0    H₀: μ₁ − μ₂ = 0
H_a: μ₁ − μ₂ > 0H₀: x₁ − x₂ = 0
H_a: x₁ − x₂ > 0

Compute the test statistic value and find the P-value. (Round your test statistic to three decimal places and your P-value to four decimal places.)

t =
P-value =

State the conclusion in the problem context.

Reject H₀. The data suggests that true average lean angle for younger females is more than that of older females.Fail to reject H₀. The data suggests that true average lean angle for younger females is more than that of older females.    Fail to reject H₀. The data suggests that true average lean angle for younger females is not more than that of older females.Reject H₀. The data suggests that true average lean angle for younger females is not more than that of older females.

Based on the 95% Confidence interval the average maximum lean angle for younger females is estimated to be  ° to  ° greater than the average maximum lean angle older females. (Round values to 2 decimal points)

Answer 1

The younger females tend to have higher maximum lean angles than older females

H₀: μ₁ − μ₂ = 0
H_a: μ₁ − μ₂ > 0

from above given data"

standard error se=√(S21/n1+S22/n2)=			1.309
test stat t =(x1-x2-Δo)/Se=		8.426
p value : =		0.0000

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

Point estimate of differnce =x1-x2=			11.033
for 95 % CI & 21 df value of t=			2.080
margin of error E=t*std error   =			2.7237
lower bound=mean difference-E=			8.3097
Upper bound=mean differnce +E=			13.7570
from above 95% confidence interval for population mean =(8.31,13.76)

Based on the 95% Confidence interval the average maximum lean angle for younger females is estimated to be   8.31 to 13.76 greater than the average maximum lean angle older females.