A recent study by Rover. com surveyed a random sample of 1500 dog owners. The research revealed that 975 of the dog owners admit to taking more photos of their dog than their significant other. Which of the following gives a 95% confidence interval for the proportion of all dog owners that would admit to taking more photos of their dog than their significant other?

Explanation:

The correct answer is (A).

The sample proportion is \hat{p} = \frac{975}{1500} = 0.65

p

^

=

1500

975

=0.65 and the z* critical value corresponding to 95% confidence is 1.96. The standard error is \sqrt{\frac{0.65(0.35)}{1500}}

1500

0.65(0.35)

, therefore the expression that gives a 95% confidence interval for the proportion of all dog owners that would admit to taking more photos of their dog than their significant other is 0.65 \pm1.96 \sqrt{\frac{0.65(0.35)}{1500}}0.65±1.96

1500

0.65(0.35)