Question

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.

(i) Which of the following statements correctly defines the null hypothesis H_O?

A.  p > 18.125 mm

B.  ? = 18.125 mm

C.  p = 18.125 mm

D.  ? > 18.125 mm

(ii) Which of the following statements correctly defines the alternate hypothesis H_A?

A.  p > 18.125 mm

B.  ? = 18.125 mm

C.  p = 18.125 mm

D.  ? > 18.125 mm

(iii) Enter the level of significance ? used for this test:

(iv) Determine sample mean x :

(v) Determine sample standard deviation s :

(vi)  Determine degrees of freedom df

(vii) Calculate and enter test statistic

(viii) Using tables, calculator, or spreadsheet: Determine and enter p-value corresponding to test statistic.

(ix) Comparing p-value and ? value, which is the correct decision to make for this hypothesis test?  

A. Reject H_o

B. Fail to reject H_o

C. Accept H_o

D. Accept H_A

(x) Select the statement that most correctly interprets the result of this test:

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.

B. The result is statistically significant at .05 level of significance. There is not enough evidence to support the claim that the mean sway forward and backward of elderly people is more than 18.125 mm, the sway of younger people.

C. The result is not 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.

D. The result is not statistically significant at .05 level of significance.   There is not enough evidence to support the claim that the mean sway forward and backward of elderly people is more than 18.125 mm, the sway of younger people.

Answer 1

1)
B. ? = 18.125 mm

2)
D. ? > 18.125 mm

3)

0.05

4)

Sample mean = 26.3333

5)
sample standard deviation = 9.7724

6)

df = n -1 = 9-1 = 8

7)
test statistics:

t = ( x - mean)/(s/sqrt(n))
= ( 26.3333 - 18.125)/(9.7724/sqrt(9))
= 2.5198

8)
p value = .0179

9)
A. Reject Ho

10)
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.