Question

Question 8 (13 points) Maintaining your balance may get harder as you grow older. A study was conducted to see how steady the elderly is on their feet. They had the subjects stand on a force platform and have them react to a noise. The force platform then measured how much they swayed forward and backward, and the data is in following table ("Maintaining balance while," 2013). Table: Forward/backward Sway (in mm) of Elderly Subjects 19 30 20 19 29 25 21 24 50 Do the data show that the elderly sway more than the mean forward sway of younger people, which is 18.125 mm? Test at the 5% level. (0) Which of the following statements correctly defines the null hypothesis Ho? A. p > 18.125 mm B. H= 18.125 mm C. p = 18.125 mm D. 4 > 18.125 mm Enter letter corresponding to correct answer (11) Which of the following statements correctly defines the alternative hypothesis HA? A. p > 18.125 mm B. u = 18.125 mm C. p = 18.125 mm D. 4 > 18.125 mm Enter letter corresponding to correct answer (iii) Enter the level of significance a used for this test: Enter in decimal form. Examples of correctly entered answers: 0.01 0.02 0.05 0.10

Answer 1

The claim is that the elderly sway is more than the mean forward sway of younger people, which is 18.125 mm. (1) The null hypothesis is H :u=18.125mm, that is, option (B) is correct. (11) The alternative hypothesis is H.: 4> 18.125mm, that is, option (D) is correct. (111) The level of significance is 5%, that is, 0.05. PhStat (Excel) is used to perform the further analysis. Steps are as; 1. Enter the data into spreadsheet. 2. Go to Add-ins>PhStat>One sample tests->t test for the mean, sigma unknown. 3. Fill the required columns as shown below;

t Test for the Mean, sigma unknown 18.125 0.05 Data Null Hypothesis: Level of Significance: Sample Statistics Options Sample Statistics Known Sample Size: Sample Mean: Sample Standard Deviation: Sample Statistics Unknown Sample Cell Range: |t1! $B$2:$B$11 - First cell contains label Test Options Two-Tail Test Upper-Tail Test Lower-Tail Test Output Options Title: Help OK Cancel

4. The result is obtained as: t Test for Hypothesis of the Mean 18.125 0.05 Data Null Hypothesis u Level of significance Sample Size Sample Mean Sample Standard Deviation 26.33333333 9.772410143 3.2575 Intermediate Calculations Standard Error of the Mean Degrees of Freedom t Test Statistic 2.5198 Upper-Tail Test Upper Critical Value p-Value Reject the null hypothesis 1.8595 0.0179 (iv) The sample mean, I is obtained as 26.3333. (v) The sample standard deviation, s is obtained as 9.7724.

(vi) The degree of freedom, df=n-1 = 9- 1 = 8. (vii) The t-test statistic is obtained as 2.5198. (viii) The p-value is obtained as 0.0179. (ix) The p-value is less than the level of significance, so, the null hypothesis is rejected. Therefore, option (A), "Reject H " is correct. (x) The option (A), “The result is statistically significant at .05 level of significance. Evidence supports the claim that the mean sway forward and backward of elderly people is more than 18.125 mm, the sway of younger people" is correct.