A university is studying the proportion of students retained in various years.Suppose the proportion of students retained in 2012 is $\text { P12 }$ and the proportion of students retained in 2013 is $P13\mathrm { P } 13$ .A study found a 90% confidence interval for $\text { P12 }$ - $P13\mathrm { P } 13$ is (-0.0398,0.0262) .Give an interpretation of this confidence interval.

A) We are 90% confident that the proportion of students retained in 2012 is between 3.98% less and 2.62% more than the proportion of students retained in 2013.
B) We know that 90% of students retained in 2013 is between 3.98% less and 2.62% more than 2012.
C) We know that 90% of students retained in 2012 is between 3.98% less and 2.62% more than 2013.
D) We are 90% confident that the proportion of students retained in 2013 is between 3.98% less and 2.62% more than the proportion of students retained in 2012.
E) We know that 90% of all random samples done on the population will show that the proportion of students retained in 2012 is between 3.98% less and 2.62% more than the proportion of students retained in 2013.

Question

A university is studying the proportion of students retained in various years.Suppose the proportion of students retained in 2012 is

\text { P12 }

and the proportion of students retained in 2013 is

P13\mathrm { P } 13

.A study found a 90% confidence interval for

\text { P12 }

-

P13\mathrm { P } 13

is (-0.0398,0.0262) .Give an interpretation of this confidence interval.

A) We are 90% confident that the proportion of students retained in 2012 is between 3.98% less and 2.62% more than the proportion of students retained in 2013.
B) We know that 90% of students retained in 2013 is between 3.98% less and 2.62% more than 2012.
C) We know that 90% of students retained in 2012 is between 3.98% less and 2.62% more than 2013.
D) We are 90% confident that the proportion of students retained in 2013 is between 3.98% less and 2.62% more than the proportion of students retained in 2012.
E) We know that 90% of all random samples done on the population will show that the proportion of students retained in 2012 is between 3.98% less and 2.62% more than the proportion of students retained in 2013.

sahera adrees · Accepted Answer

Final Answer : A, Explanation :   The confidence interval for   P12 − P13 	ext{P12} - 	ext{P13} P12 − P13   being (-0.0398, 0.0262) means we are 90% confident that the true difference in proportions (2012's retention rate minus 2013's retention rate) lies within this interval. This translates to the retention rate in 2012 being anywhere from 3.98% lower to 2.62% higher than in 2013.

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