cmi-entrance 2024 Q14

cmi-entrance · India · mscds Not Maths
14. A prominent newspaper conducted a survey among a carefully chosen sample of $1,00,000$ voters under the age of 25 . A randomly chosen subset of $60 \%$ of this sample were asked the following question: "Have you ever voted in a general election?" The remaining $40 \%$ were asked the following, different question: "Is it true that you have never voted in a general election?" The editor in charge of collating the data from the survey, accidentally deleted some of the contents of the survey database. The only information that survived this mishap was that a total of 54,000 respondents replied Yes to the question that they got. Specifically, it is not known how many of these Yes answers correspond to the first question, and how many to the second.
Assume that the sampling was done properly and that the respondents answered truthfully. What estimate can we derive from just the total number of Yes answers, about the percentage of voters under the age of 25 that have voted in some general election?
(a) At most $30 \%$.
(b) More than $30 \%$, but less than $60 \%$.
(c) At least $60 \%$, but less than $75 \%$.
(d) No such estimate can be drawn from just the total number of Yes answers.
14. A prominent newspaper conducted a survey among a carefully chosen sample of $1,00,000$ voters under the age of 25 . A randomly chosen subset of $60 \%$ of this sample were asked the following question: "Have you ever voted in a general election?" The remaining $40 \%$ were asked the following, different question:\\
"Is it true that you have never voted in a general election?"\\
The editor in charge of collating the data from the survey, accidentally deleted some of the contents of the survey database. The only information that survived this mishap was that a total of 54,000 respondents replied Yes to the question that they got. Specifically, it is not known how many of these Yes answers correspond to the first question, and how many to the second.

Assume that the sampling was done properly and that the respondents answered truthfully. What estimate can we derive from just the total number of Yes answers, about the percentage of voters under the age of 25 that have voted in some general election?\\
(a) At most $30 \%$.\\
(b) More than $30 \%$, but less than $60 \%$.\\
(c) At least $60 \%$, but less than $75 \%$.\\
(d) No such estimate can be drawn from just the total number of Yes answers.\\