Could you please help me, thanks!
(i) (ii) (iii) How difcult is it to maintain your balance while concentrating? Is it more difcult when you are older? Nineteen elderly and nineteen young men were subjects in an experiment. Each subject stood barefoot on a "force platform" and was asked to maintain a stable upright position and to react as quickly as possible to an unpredictable noise by pressing a hand held button. The noise came randomly and the subject concentrated on reacting as quickly as possible. The platform automatically measured how much each subject swayed in millimetres in both the forwardfbackward and the side-to-side directions. The data is given below. Elderly (x) Construct a back-to-back stem and leaf plot for this data. Describe the distribution of the two sets of data. [8] The sample means and sample standard deviations of the two groups are provided in the table overleaf. Carry out a formal test of equality of population variances, giving full details (including assumptions, hypotheses, test statistic, rejection region, test decision and conclusion). [10] At a 5% level of signicance test if the mean sway is different for the young and elderly. Use the appropriate MIN ITAB output to report the results of the test. Provide full details including assumptions, hypotheses, test statistic and p-value, test decision and conclusion. [7] [MINITAB output for Question 1 overleaf...] MINITAB Outputs Q1 Statistics Variable N Mean SE Mean StDev Minimum Q1 Median Q3 Maximum Elderly 19 27.95 1.58 6.88 19.00 23.00 27.00 31.00 41.00 Young 19 20.526 0.965 4.208 14.000 17.000 21.000 23.000 28.000 Method 1 Method 2 M1: mean of Elderly M1: mean of Elderly H2: mean of Young H2: mean of Young Difference: M1 - H2 Difference: M1 - H2 Equal variances are assumed for this analysis. Equal variances are assumed for this analysis. Estimation for Difference Estimation for Difference Pooled 95% Lower Bound Pooled 95% CI for Difference StDev for Difference Difference StDev Difference 7.42 5.70 4.30 7.42 5.70 (3.67, 11.17) Test Test Null hypothesis Ho: H1 - H2 = 0 Null hypothesis Ho: H1 - H2 = 0 Alternative hypothesis H1: 1 - H2 > 0 Alternative hypothesis H1: 1 - H2 # 0 T-Value DF P-Value T-Value DF P-Value 4.01 36 0.000 4.01 36 0.000 Method 3 Method 4 M1: mean of Elderly M1: mean of Elderly H2: mean of Young H2: mean of Young Difference: M1 - H2 Difference: M1 - H2 Equal variances are not assumed for this analysis Equal variances are not assumed for this analysis Estimation for Difference Estimation for Difference 95% Lower Bound 95% CI for Difference for Difference Difference Difference 7.42 4.28 7.42 (3.64, 11.21) Test Test Null hypothesis Ho: M1 - 2 = 0 Null hypothesis Ho: H1 - H2 = 0 Alternative hypothesis H1: 1 1 - H2 > 0 Alternative hypothesis H1: H1 - H2 # 0 T-Value DF P-Value T-Value DF P-Value 4.01 29 0.000 4.01 29 0.000 [Question 2 overleaf...]
