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 28, 34, 33, 27, 28, 32, 31, 36, 32, 28, 29, 37, 29, 34, 33, 27, 28, 32, 31, 34) OF c 23, 18, 22, 23, 22, 17, 14, 26, 17, 15, 22, 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 younger females tend to have higher maximum lean angles than older females O The maximum lean angle is approximately the same for younger and older females O The older females tend to have higher maximum lean angles than younger 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.) Ha: X1-X2>0 0: H1H20 Ho: 1 -H20 Ha: μ1-μ2 > 0 Ha: 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.) P-value- State the conclusion in the problem context. 0 Reject H0. The data suggests that true average lean angle for younger females is more than that of older females Fail to reject Ho. The data suggests that true average lean angle for younger females is more than that of older females O Reject Ho. The data suggests that true average lean angle for younger females is not more than that of Fail to reject Ho. 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 greater than the average maximum lean angle older females. (Round values to 2 decimal points) You may need to use the t-table to complete this problem

Answer 1

Which of the following is true based on the side by side box plot of the data? 1st option is correct.

$H_0: \mu_1 - \mu_2 = 0, H_a: \mu_1 - \mu_2 > 0$ (3rd option is correct).

t = 8.950, p-value = 0.0000
Conclusion: 1st option is correct.

95% confidence interval = (8.80, 14.16).