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 1% level. forward sway in mm 34 30 31 34 24 25 22 33 33 17 19 29 30 31 24 33 27 26 26 30 17 17 15 41 48 34 15 36 20 9 34 12 13 34 14 29 39 33 11 20 25 29 23 27 A: Assumptions Since information was collected from each object, what conditions do we need to check? Check all that apply. n(pˆ)≥10n(p̂)≥10 np≥10np≥10 n(1−p)≥10n(1-p)≥10 σσ is unknown n(1−pˆ)≥10n(1-p̂)≥10 σσ is known n≥30n≥30 or normal population N≥20nN≥20n no outliers in the data outliers in the data Check those assumptions: 1. Is the value of σσ known? 2. Given the following modified boxplot (If using a screenreader, use technology to generate a boxplot, then asnwer the question below): (5101520253035404550forward sway in mm919.5273348[Graphs generated by this script: setBorder(15); initPicture(5,50,-3,6);axes(5,100,1,null,null,1,'off');text([24.5,-3],"forward sway in mm");line([9,2],[9,4]); rect([19.5,2],[33,4]); line([27,2],[27,4]);line([48,2],[48,4]); line([9,3],[19.5,3]); line([33,3],[48,3]);fontsize*=.8;fontfill='blue';text([9,4],'9','above');text([19.5,4],'19.5','above');text([27,4],'27','above');text([33,4],'33','above');text([48,4],'48','above');fontfill='black';fontsize*=1.25;]) Are there any outliers? 3. nn = which is Is it reasonable to assume the population is normally distributed? N: Name the test The conditions are met to use a . T: Test Statistic The symbol and value of the random variable on this problem are as follows: = mm The test statistic formula set up with numbers is as follows: Round values to 2 decimal places. t=¯¯¯X−μs√n=t=X¯-μsn= (((( −- )) // /√/ )))) The final answer for the test statistic from technology is as follows: Round to 2 decimal places. t =
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 1% level.
| forward sway in mm |
|---|
| 34 |
| 30 |
| 31 |
| 34 |
| 24 |
| 25 |
| 22 |
| 33 |
| 33 |
| 17 |
| 19 |
| 29 |
| 30 |
| 31 |
| 24 |
| 33 |
| 27 |
| 26 |
| 26 |
| 30 |
| 17 |
| 17 |
| 15 |
| 41 |
| 48 |
| 34 |
| 15 |
| 36 |
| 20 |
| 9 |
| 34 |
| 12 |
| 13 |
| 34 |
| 14 |
| 29 |
| 39 |
| 33 |
| 11 |
| 20 |
| 25 |
| 29 |
| 23 |
| 27 |
A: Assumptions
Since information was collected from each object, what conditions do we need to check?
Check all that apply.
- n(pˆ)≥10n(p̂)≥10
- np≥10np≥10
- n(1−p)≥10n(1-p)≥10
- σσ is unknown
- n(1−pˆ)≥10n(1-p̂)≥10
- σσ is known
- n≥30n≥30 or normal population
- N≥20nN≥20n
- no outliers in the data
- outliers in the data
Check those assumptions:
1. Is the value of σσ known?
2. Given the following modified boxplot (If using a screenreader, use technology to generate a boxplot, then asnwer the question below):
(5101520253035404550forward sway in mm919.5273348[Graphs generated by this script: setBorder(15); initPicture(5,50,-3,6);axes(5,100,1,null,null,1,'off');text([24.5,-3],"forward sway in mm");line([9,2],[9,4]); rect([19.5,2],[33,4]); line([27,2],[27,4]);line([48,2],[48,4]); line([9,3],[19.5,3]); line([33,3],[48,3]);fontsize*=.8;fontfill='blue';text([9,4],'9','above');text([19.5,4],'19.5','above');text([27,4],'27','above');text([33,4],'33','above');text([48,4],'48','above');fontfill='black';fontsize*=1.25;])
Are there any outliers?
3. nn = which is
Is it reasonable to assume the population is normally distributed?
N: Name the test
The conditions are met to use a .
T: Test Statistic
The symbol and value of the random variable on this problem are as follows:
= mm
The test statistic formula set up with numbers is as follows:
Round values to 2 decimal places.
t=¯¯¯X−μs√n=t=X¯-μsn=
(((( −- )) // /√/ ))))
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 .
S: State a conclustion
There significant evidence to conclude mm
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