You want to estimate the proportion of all passengers who survived the Titanic. You do not have time to research every single passenger, so you decide to use stratified random sampling based on class (1* 2nd, or 3rd). Titanic had a total of 320 1* class passengers, 285 2nd class passengers, and 706 passengers in 3rd class. Here is a summary of the data you collected: Rows: Class Columns: Survived No Yes All 1st Class 9 11 20 2nd Class 6 5 11 3rd Class 27 7 34 All 42 23 65 For example, looking at the table above you can see that you randomly sampled 20 passengers from 1* class and found that 11 of them survived. a. Use stratified random sampling to estimate the proportion of all Titanic passengers who survived, and place a bound on the error of estimation. Use three decimals. b. The actual population proportion for Titanic passengers who survived was 38.44%. Without knowing the true value for p, would you have concluded that p = 38.44% was likely, given your results for part (a)? Explain your answer.

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You want to estimate the proportion of all passengers who survived the Titanic. You do not have
time to research every single passenger, so you decide to use stratified random sampling based
on class (1* 2nd, or 3rd). Titanic had a total of 320 1* class passengers, 285 2nd class passengers,
and 706 passengers in 3rd class. Here is a summary of the data you collected:
Rows: Class Columns: Survived
No Yes All
1st Class
9 11 20
2nd Class
6 5 11
3rd Class
27
7 34
All
42 23 65
For example, looking at the table above you can see that you randomly sampled 20 passengers
from 1* class and found that 11 of them survived.
a. Use stratified random sampling to estimate the proportion of all Titanic passengers who
survived, and place a bound on the error of estimation. Use three decimals.
b. The actual population proportion for Titanic passengers who survived was 38.44%. Without
knowing the true value for p, would you have concluded that p = 38.44% was likely, given your
results for part (a)? Explain your answer.
Transcribed Image Text:You want to estimate the proportion of all passengers who survived the Titanic. You do not have time to research every single passenger, so you decide to use stratified random sampling based on class (1* 2nd, or 3rd). Titanic had a total of 320 1* class passengers, 285 2nd class passengers, and 706 passengers in 3rd class. Here is a summary of the data you collected: Rows: Class Columns: Survived No Yes All 1st Class 9 11 20 2nd Class 6 5 11 3rd Class 27 7 34 All 42 23 65 For example, looking at the table above you can see that you randomly sampled 20 passengers from 1* class and found that 11 of them survived. a. Use stratified random sampling to estimate the proportion of all Titanic passengers who survived, and place a bound on the error of estimation. Use three decimals. b. The actual population proportion for Titanic passengers who survived was 38.44%. Without knowing the true value for p, would you have concluded that p = 38.44% was likely, given your results for part (a)? Explain your answer.
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