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Maintaining your balance may get harder as you grow older. A study was conducted to see how steady the elderly are on their feet. They had a random sample of 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 are in the table below. Do the data show that the mean elderly sway measurement is higher than the mean forward sway of younger people, which is 18.125 mm? Test at the 5% level.

forward sway in mm

36

18

37

27

25

10

23

19

34

28

24

24

5

18

20

17

25

36

42

29

25

21

35

30

26

32

14

25

33

22

33

31

18

20

22

25

26

34

40

17

22

11

26

25

P: Parameter

What is the correct parameter symbol for this problem? ? N p s X p X n Incorrect What is the wording of the parameter in the context of this problem? Select an answer The mean forward sway of all elderly people All elderly people A randomly selected elderly person The mean forward sway in 44 randomly selected elderly people The forward sway of a randomly selected elderly person 44 randomly selected elderly people Incorrect H: Hypotheses

Fill in the correct null and alternative hypotheses:

H0:H0: ? N n p s X p X ? < = > mm HA:HA: ? X N p p n s X ? < = > mm

A: Assumptions

Since Select an answer quantitative qualitative information was collected from each object, what conditions do we need to check?

Check all that apply.

• no outliers in the data
• is known
• is unknown
• N20nN20n
• n30n30 or normal population
• np10np10
• n(1p)10n(1-p)10
• n(1p)10n(1-p)10
• n(p)10n(p)10
• outliers in the data

Check those assumptions: 1. Is the value of known? ? no yes

2. Which of the following is the correct modified boxplot?

51015202530354045forward sway in mm512.52531.542[Graphs generated by this script: setBorder(15); initPicture(5,45,-3,6);axes(5,100,1,null,null,1,'off');text([23.5,-3],"forward sway in mm");line([5,2],[5,4]); rect([12.5,2],[31.5,4]); line([25,2],[25,4]);line([42,2],[42,4]); line([5,3],[12.5,3]); line([31.5,3],[42,3]);fontsize*=.8;fontfill='blue';text([5,4],'5','above');text([12.5,4],'12.5','above');text([25,4],'25','above');text([31.5,4],'31.5','above');text([42,4],'42','above');fontfill='black';fontsize*=1.25;] 51015202530354045forward sway in mm5202536.7542[Graphs generated by this script: setBorder(15); initPicture(5,45,-3,6);axes(5,100,1,null,null,1,'off');text([23.5,-3],"forward sway in mm");line([5,2],[5,4]); rect([20,2],[36.75,4]); line([25,2],[25,4]);line([42,2],[42,4]); line([5,3],[20,3]); line([36.75,3],[42,3]);fontsize*=.8;fontfill='blue';text([5,4],'5','above');text([20,4],'20','above');text([25,4],'25','above');text([36.75,4],'36.75','above');text([42,4],'42','above');fontfill='black';fontsize*=1.25;] 51015202530354045forward sway in mm5202531.542[Graphs generated by this script: setBorder(15); initPicture(5,45,-3,6);axes(5,100,1,null,null,1,'off');text([23.5,-3],"forward sway in mm");line([5,2],[5,4]); rect([20,2],[31.5,4]); line([25,2],[25,4]);line([42,2],[42,4]); line([5,3],[20,3]); line([31.5,3],[42,3]);fontsize*=.8;fontfill='blue';text([5,4],'5','above');text([20,4],'20','above');text([25,4],'25','above');text([31.5,4],'31.5','above');text([42,4],'42','above');fontfill='black';fontsize*=1.25;] 51015202530354045forward sway in mm52022.531.542[Graphs generated by this script: setBorder(15); initPicture(5,45,-3,6);axes(5,100,1,null,null,1,'off');text([23.5,-3],"forward sway in mm");line([5,2],[5,4]); rect([20,2],[31.5,4]); line([22.5,2],[22.5,4]);line([42,2],[42,4]); line([5,3],[20,3]); line([31.5,3],[42,3]);fontsize*=.8;fontfill='blue';text([5,4],'5','above');text([20,4],'20','above');text([22.5,4],'22.5','above');text([31.5,4],'31.5','above');text([42,4],'42','above');fontfill='black';fontsize*=1.25;]

Are there any outliers? Select an answer Yes, the modified boxplot shows outliers. Yes, the histogram shows outliers. No, the modified boxplot shows no outliers. Yes, the normal probability plot shows outliers. No, the histogram shows no outliers. No, the normal probability plot shows no outliers.

3. nn = which is ? < Is it reasonable to assume the population is normally distributed? Select an answer Not necessary to check since the sample size is at least 30. Not necessary to check since the sample size is less than 30. Yes since the normal probability plot is roughly linear with no outliers. Yes since the normal probability plot is roughly bell-shaped with no outliers. No, since the normal probability plot is not roughly linear. No, since the normal probability plot is not roughly bell-shaped. N: Name the test

The conditions are met to use a Select an answer 2-Sample T-Test 1-Proportion Z-Test Paired T-Test 2-Proportion Z-Test T-Test . T: Test Statistic

The symbol and value of the random variable on this problem are as follows: ? p p X X s N n = mm

The test statistic formula set up with numbers is as follows:

Round values to 2 decimal places. t=Xsn=t=X-sn= (((( - )) // // ))))

The final answer for the test statistic from technology is as follows:

Round to 2 decimal places.

t = O: Obtain the P-value

Report the final answer to 4 decimal places.

It is possible when rounded that a p-value is 0.0000 P-value = M: Make a decision

Since the p-value ? = < > , we Select an answer reject H fail to reject H accept H reject H fail to reject H . S: State a conclustion

There Select an answer is is not significant evidence to conclude Select an answer a randomly selected elderly person the mean forward sway of all elderly people all elderly people the mean forward sway in 44 randomly selected elderly people the forward sway of a randomly selected elderly person 44 randomly selected elderly people Select an answer is less than is equal to is more than differs from mm