Suppose the proportion of women who watch CBC News is $PW\mathrm { P } _ { \mathrm { W } }$ and the proportion of men who watch CBC News is $Pm\mathrm { Pm }$ .The survey found a 95% confidence interval for $p _ { W } - p _ { m }$ is $(- 0.06, 0.25)$ Give an interpretation of this confidence interval.

A) We are 95% confident that the proportion of women who watch CBC News is between 6% lower and 25% higher than the proportion of men who watch CBC News.
B) We know that 95% of all random samples done on the population will show that the proportion of men who watch CBC News is between 6% lower and 25% higher than the proportion of women who watch CBC News.
C) We know that 95% of all random samples done on the population will show that the proportion of women who watch CBC News is between 6% lower and 25% higher than the proportion of men who watch CBC News.
D) We are 95% confident that the proportion of men who watch CBC News is between 6% lower and 25% higher than the proportion of women who watch CBC News.
E) 95% of men and women watch CBC News 6% less to 25% more than other news programs.

Question

Suppose the proportion of women who watch CBC News is

PW\mathrm { P } _ { \mathrm { W } }

and the proportion of men who watch CBC News is

Pm\mathrm { Pm }

.The survey found a 95% confidence interval for

p _ { W } - p _ { m }

is

(- 0.06, 0.25)

Give an interpretation of this confidence interval.

A) We are 95% confident that the proportion of women who watch CBC News is between 6% lower and 25% higher than the proportion of men who watch CBC News.
B) We know that 95% of all random samples done on the population will show that the proportion of men who watch CBC News is between 6% lower and 25% higher than the proportion of women who watch CBC News.
C) We know that 95% of all random samples done on the population will show that the proportion of women who watch CBC News is between 6% lower and 25% higher than the proportion of men who watch CBC News.
D) We are 95% confident that the proportion of men who watch CBC News is between 6% lower and 25% higher than the proportion of women who watch CBC News.
E) 95% of men and women watch CBC News 6% less to 25% more than other news programs.

#MissJayy TheMUA · Accepted Answer

Final Answer : A, Explanation :   The confidence interval for   p W − p m p _ { W } - p _ { m } p W ​ − p m ​   from   ( − 0.06 , 0.25 ) (-0.06, 0.25) ( − 0.06 , 0.25 )   suggests that we are 95% confident the true difference in proportions (women's proportion minus men's proportion) falls within this range, indicating women's viewership could be from 6% lower to 25% higher than men's.

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