A marketing survey involves product recognition in Ontario and British Columbia.Suppose the proportion of Ontario residents who recognized a product is $P1\mathrm { P } 1$ and the proportion of British Columbia residents who recognized the product is $P2\mathrm { P } 2$ .The survey found a 98% confidence interval for $p _ { 1 } - p _ { 2 }$ is $(- 0.023, - 0.019)$ Give an interpretation of this confidence interval.

A) We know that 98% of British Columbia residents recognized the product between 1.9% and 2.3% more often than Ontario residents.
B) We know that 98% of Ontario residents recognized the product between 1.9% and 2.3% more often than British Columbia residents.
C) We are 98% confident that the proportion of British Columbia residents who recognized the product is between 1.9% and 2.3% higher than the proportion of Ontario residents who recognized the product.
D) We know that 98% of all random samples done on the population will show that the proportion of British Columbia residents who knew the product is between 1.9% and 2.3% higher than the proportion of Ontario residents who knew the product.
E) We are 98% confident that the proportion of Ontario residents who recognized the product is between 1.9% and 2.3% higher than the proportion of British Columbia residents who recognized the product.

Question

A marketing survey involves product recognition in Ontario and British Columbia.Suppose the proportion of Ontario residents who recognized a product is

P1\mathrm { P } 1

and the proportion of British Columbia residents who recognized the product is

P2\mathrm { P } 2

.The survey found a 98% confidence interval for

p _ { 1 } - p _ { 2 }

is

(- 0.023, - 0.019)

Give an interpretation of this confidence interval.

A) We know that 98% of British Columbia residents recognized the product between 1.9% and 2.3% more often than Ontario residents.
B) We know that 98% of Ontario residents recognized the product between 1.9% and 2.3% more often than British Columbia residents.
C) We are 98% confident that the proportion of British Columbia residents who recognized the product is between 1.9% and 2.3% higher than the proportion of Ontario residents who recognized the product.
D) We know that 98% of all random samples done on the population will show that the proportion of British Columbia residents who knew the product is between 1.9% and 2.3% higher than the proportion of Ontario residents who knew the product.
E) We are 98% confident that the proportion of Ontario residents who recognized the product is between 1.9% and 2.3% higher than the proportion of British Columbia residents who recognized the product.

Sandy Sidhu · Accepted Answer

Final Answer : C, Explanation :  The confidence interval tells us that we can be 98% confident that the true proportion of British Columbia residents who recognized the product is between 1.9% and 2.3% higher than the proportion of Ontario residents who recognized the product. This interpretation is consistent with the given information about the proportions in each province. Options A, B, and E are incorrect because they make claims that are not supported by the information given or the confidence interval provided. Option D is also incorrect because it makes a broad and unsupported claim about all possible samples, rather than the specific confidence interval obtained from this survey.

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