Problem 4.

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 the table below.

Table: Forward/backward Sway (in mm) of Elderly Subjects

19

30

20

19

29

25

21

24

50

Set up and run a test of hypothesis to determine if the elderly swaymore than the mean forward sway of younger people, which is 18.125 mm?Use a level of significance of 5%.Specifically, do the following:

(i)Write down the null and alternative hypotheses.

(ii)Verify that the assumptions necessary to apply the test are satisfied.

(iii)What is the test statistic and what is the p-value?

(iv)State your conclusion.