Suppose the proportion of people losing weight at a city weight loss centre is $PC\mathrm { P } _ { \mathrm { C } }$ and the proportion of people losing weight at a suburban weight loss centre is $p _ { s }$ .A study found a 98% confidence interval for $PC\mathrm { P } _ { \mathrm { C } }$ - $p _ { s }$ is (-0.1263,0.0891) .Give an interpretation of this confidence interval.

A) We are 98% confident that the proportion of people losing weight at the city weight loss centre is between 12.63% less and 8.91% more than the proportion of people losing weight at the suburban weight loss centre.
B) We know that 98% of the people at the suburban weight loss centre lost between 12.63% less and 8.91% more than the people at the city weight loss centre.
C) We know that 98% of all random samples done on the population will show that the proportion of people losing weight at the city weight loss centre is between 12.63% less and 8.91% more than the proportion of people losing weight at the suburban weight loss centre.
D) We are 98% confident that the proportion of people losing weight at the suburban weight loss centre is between 12.63% less and 8.91% more than the proportion of people losing weight at the city weight loss centre.
E) We know that 98% of the people at the city weight loss centre lost between 12.63% less and 8.91% more than the people at the suburban weight loss centre.

Question

Suppose the proportion of people losing weight at a city weight loss centre is

PC\mathrm { P } _ { \mathrm { C } }

and the proportion of people losing weight at a suburban weight loss centre is

p _ { s }

.A study found a 98% confidence interval for

PC\mathrm { P } _ { \mathrm { C } }

-

p _ { s }

is (-0.1263,0.0891) .Give an interpretation of this confidence interval.

A) We are 98% confident that the proportion of people losing weight at the city weight loss centre is between 12.63% less and 8.91% more than the proportion of people losing weight at the suburban weight loss centre.
B) We know that 98% of the people at the suburban weight loss centre lost between 12.63% less and 8.91% more than the people at the city weight loss centre.
C) We know that 98% of all random samples done on the population will show that the proportion of people losing weight at the city weight loss centre is between 12.63% less and 8.91% more than the proportion of people losing weight at the suburban weight loss centre.
D) We are 98% confident that the proportion of people losing weight at the suburban weight loss centre is between 12.63% less and 8.91% more than the proportion of people losing weight at the city weight loss centre.
E) We know that 98% of the people at the city weight loss centre lost between 12.63% less and 8.91% more than the people at the suburban weight loss centre.

Denisse Hernandez · Accepted Answer

Final Answer : A, Explanation :  The confidence interval tells us that we are 98% confident that the true difference in proportions (city - suburban) is between -0.1263 and 0.0891. Since the interval includes negative values, it is possible that the proportion of people losing weight at the city center is lower than the proportion at the suburban center. Therefore, the best interpretation is that we are 98% confident that the proportion of people losing weight at the city weight loss center is between 12.63% less and 8.91% more than the proportion of people losing weight at the suburban weight loss center.

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