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vinyasgupta
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If the margin of error is already given in %, to get the overall error in absolute terms, you need to weight it by both:
  • The proportion of that subgroup within the total.
  • The total population size.

If you're only comparing within the subgroup (relative error), the total strength factor is dropped
imRaj

chetan2u
hi vinay,
the third question talks of two things..
1) overall error of margin... it will be equal to the sum of (all margin error *respective percentage*total strength)
2) relative to its own total customer base... it means we are interested in only the percentage and not number..
combine the two ..... now it means the sum of (all margin error *respective percentage)....
if we look at the armed forces right below it(also provided in OE), you can see it has higher margin of error and higher % in each category so atleast armed forces has 'the overal margin.......customer base' more than agriculture ,so false...
­Hi chetan2u ! Just wanted to check a small doubt of mine. Here margin of error mentioned in the graph has units in %age, right? That's why u r multiplying it with respective percentage*total strength, right?
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Please explain, why statement "Assuming actual values are within the margin of error, it is possible that a larger proportion of people drove alone to work in the armed forces than drove alone to work in construction." is true?
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Drove alone % and margins of error:
-Armed forces: 74.4% ± 0.9 → range: 73.5% to 75.3%
-Construction: 75.1% ± 0.3 → range: 74.8% to 75.4%

Armed forces max: 75.3%
Construction min: 74.8%

Overlap exists (75.3% > 74.8%), so it’s possible Armed forces could be higher as we do not know the difference between the two.
PrafulLata
Please explain, why statement "Assuming actual values are within the margin of error, it is possible that a larger proportion of people drove alone to work in the armed forces than drove alone to work in construction." is true?
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Can anyone help me with this one?
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1. "The median margin of error for walking is larger than the mode margin of error for walking."
  • Walking margins of error: 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.2, 0.2, 0.1, 0.1, 0.2, 0.7
  • Mode = 0.1 (appears most often)
  • Median = middle value when sorted = 0.1
  • Conclusion: Median (0.1) is not larger than mode (0.1). = False

2. "Assuming actual values are within the margin of error, it is possible that a larger proportion of people drove alone to work in the armed forces than drove alone to work in construction."
  • Armed forces: drove alone = 74.4% ± 0.9 = possible range: 73.5% to 75.3%
  • Construction: drove alone = 75.1% ± 0.3 = possible range: 74.8% to 75.4%
  • Max for armed forces = 75.3%
  • Min for construction = 74.8%
  • Since 75.3% > 74.8%, it's possible armed forces could be higher. = True

3. "The listed industry with the largest overall margin of error relative to its own total commuters is agriculture, forestry, and mining."
  • We check the largest margin of error across all travel types for each industry, then compare relative to total commuters.
  • Agriculture, forestry, and mining: total commuters = 2,168. largest margin of error = 0.7 (walking = 0.2, all other means = 0.3, biggest is drove alone = 0.7) → 0.7 / 2168 is large proportionally, but...
  • Armed forces: total commuters = 1,174; largest margin of error = 0.9 (drove alone) = 0.9 / 1174 is even larger proportionally.
  • So the statement is False.

vinyasgupta
Attachment:
T.png
Attachment:
Q.png
The table provides information from a statistical analysis of data on commuter travel in 2009. "Commuter" in this case is defined as any worker who does not work from home. In addition to the study's findings on methods of travel used by employees in different industries, the table provides the statistical margin of error of the findings. This number, when added to or subtracted from the estimate, represents the 90 percent confidence interval around the estimate.
--
(Sort ↕ the table by clicking on the headers)
Drove alone
Carpooled
Public transportation
Walked
All other means
IndustryTotal

commuters
(in
thousands)
PercentMargin
of error

(+/-)
PercentMargin
of error

(+/-)
PercentMargin
of error

(+/-)
PercentMargin
of error

(+/-)
PercentMargin
of error

(+/-)
Education and health

care
29,92180.90.19.40.14.80.13.50.11.40.1
Finance and insurance8,93380.90.27.20.18.20.22.70.110.1
Manufacturing14,08683.30.211.30.22.50.11.40.11.50.1
Public administration6,58982.10.28.90.26.40.21.40.11.30.1
Retail trade15,49381.50.29.10.14.40.13.30.11.70.1
Scientific and

management
13,30176.60.210.90.280.12.50.12.10.1
Transportation and

warehousing
6,68383.70.28.30.23.80.11.30.130.1
Construction8,84175.10.318.50.32.90.11.40.12.10.1
Entertainment and

recreation
12,28172.30.312.00.27.40.25.60.12.70.1
Other services6,44977.60.310.40.25.90.24.30.11.80.1
Wholesale trade3,80284.40.39.40.33.20.21.60.11.40.1
Information2,95279.10.48.10.38.20.32.70.21.90.1
Agriculture, forestry,

and mining
2,16872.40.717.00.51.90.25.30.23.40.3
Armed forces1,17474.40.910.90.61.50.210.10.73.10.3

Consider the following statements. On the basis of the data provided, indicate whether each statement is true or false.
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Thank you for the detailed explanation
cheshire
1. "The median margin of error for walking is larger than the mode margin of error for walking."
  • Walking margins of error: 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.2, 0.2, 0.1, 0.1, 0.2, 0.7
  • Mode = 0.1 (appears most often)
  • Median = middle value when sorted = 0.1
  • Conclusion: Median (0.1) is not larger than mode (0.1). = False

2. "Assuming actual values are within the margin of error, it is possible that a larger proportion of people drove alone to work in the armed forces than drove alone to work in construction."
  • Armed forces: drove alone = 74.4% ± 0.9 = possible range: 73.5% to 75.3%
  • Construction: drove alone = 75.1% ± 0.3 = possible range: 74.8% to 75.4%
  • Max for armed forces = 75.3%
  • Min for construction = 74.8%
  • Since 75.3% > 74.8%, it's possible armed forces could be higher. = True

3. "The listed industry with the largest overall margin of error relative to its own total commuters is agriculture, forestry, and mining."
  • We check the largest margin of error across all travel types for each industry, then compare relative to total commuters.
  • Agriculture, forestry, and mining: total commuters = 2,168. largest margin of error = 0.7 (walking = 0.2, all other means = 0.3, biggest is drove alone = 0.7) → 0.7 / 2168 is large proportionally, but...
  • Armed forces: total commuters = 1,174; largest margin of error = 0.9 (drove alone) = 0.9 / 1174 is even larger proportionally.
  • So the statement is False.

vinyasgupta
Attachment:
T.png
Attachment:
Q.png
The table provides information from a statistical analysis of data on commuter travel in 2009. "Commuter" in this case is defined as any worker who does not work from home. In addition to the study's findings on methods of travel used by employees in different industries, the table provides the statistical margin of error of the findings. This number, when added to or subtracted from the estimate, represents the 90 percent confidence interval around the estimate.
--
(Sort ↕ the table by clicking on the headers)
Drove alone
Carpooled
Public transportation
Walked
All other means
IndustryTotal

commuters
(in
thousands)
PercentMargin
of error

(+/-)
PercentMargin
of error

(+/-)
PercentMargin
of error

(+/-)
PercentMargin
of error

(+/-)
PercentMargin
of error

(+/-)
Education and health

care
29,92180.90.19.40.14.80.13.50.11.40.1
Finance and insurance8,93380.90.27.20.18.20.22.70.110.1
Manufacturing14,08683.30.211.30.22.50.11.40.11.50.1
Public administration6,58982.10.28.90.26.40.21.40.11.30.1
Retail trade15,49381.50.29.10.14.40.13.30.11.70.1
Scientific and

management
13,30176.60.210.90.280.12.50.12.10.1
Transportation and

warehousing
6,68383.70.28.30.23.80.11.30.130.1
Construction8,84175.10.318.50.32.90.11.40.12.10.1
Entertainment and

recreation
12,28172.30.312.00.27.40.25.60.12.70.1
Other services6,44977.60.310.40.25.90.24.30.11.80.1
Wholesale trade3,80284.40.39.40.33.20.21.60.11.40.1
Information2,95279.10.48.10.38.20.32.70.21.90.1
Agriculture, forestry,

and mining
2,16872.40.717.00.51.90.25.30.23.40.3
Armed forces1,17474.40.910.90.61.50.210.10.73.10.3

Consider the following statements. On the basis of the data provided, indicate whether each statement is true or false.
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