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, 32, 27, 28, 32, 31, 35, 32, 29 OF: 18, 15, 21, 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 mu_1 for younger females and mu_2 for older females.) H_0 middot mu_1 - mu_2 = 10 H_a middot mu_1 - mu_2 0 H_0 middot mu_1 - mu_2 = 10 H_a middot mu_1 - mu_2 > 10 H_0 middot mu_1 - mu_2 = 0 H_a middot mu_1 - mu_2

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   =   10  
Ha:   u1 - u2   >   10   [ANSWER, C]

********************************

b)

At level of significance =    0.1          
As we can see, this is a    right   tailed test.      
Calculating the means of each group,              
              
X1 =    31.1          
X2 =    15.8          
              
Calculating the standard deviations of each group,              
              
s1 =    2.923088169          
s2 =    3.701351105          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    10          
n2 = sample size of group 2 =    5          
Thus, df = n1 + n2 - 2 =    13          
Also, sD =    1.895902013          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    2.795503123   [ANSWER, TEST STATISTIC]

****************************

c)      
              
where uD = hypothesized difference =    10          
Also, using p values, as this is right tailed,              
              
p =    0.007579819   [ANSWER]

**************************

d)

As P < 0.1,

OPTION D: Reject Ho. The data suggests that the true average lean for older females is more than 10 dgerees smaller than that of younger females. [ANSWER, D]

*****************************************************

Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.