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, 35, 32, 27, 28, 32, 31, 36, 32, 27 OF: 17, 14, 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.) 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 =

Explanation / Answer

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   <=   10  
Ha:   u1 - u2   >   10  
At level of significance =    0.1          
As we can see, this is a    right   tailed test.      
Calculating the means of each group,              
              
X1 =    30.9          
X2 =    15.4          
              
Calculating the standard deviations of each group,              
              
s1 =    3.142893218          
s2 =    3.646916506          
              
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 =    1.909915647          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    2.879708331   [ANSWER TEST STATISTIC]

****************************************************      
Also, using p values, as this is right tailed,              
              
p =    0.006450307   [ANSWER, P VALUE]

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

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.