Question

(1 point)
an environmentalist wishes to survey canadians to determine what percentage support strict environmental controls on the oil and gas industry
the environmentalist randomly picks ( n = 700 ) canadians, and finds that 484 favour strict environmental controls on the oil and gas industry
(a) find a 95% confidence interval for ( p ) without using a bootstrap sample. use at least four decimal points for your lower and upper bounds.
lower bound ( = 0.6371 )
upper bound ( = 0.7257 )
(b) interpret the meaning of the interval you found in part (a).
the proportion of all canadians who support strict environmental controls on the oil and gas industry is and (enter your answer to at least two decimals.)

Explanation:

A confidence interval gives a range of values within which the true population parameter (in this case, the proportion \(p\) of Canadians who support strict environmental controls on the Oil and Gas Industry) is likely to lie. A 95% confidence interval means that if we were to take many samples and construct confidence intervals in the same way, approximately 95% of those intervals would contain the true population proportion.

In part (a), the interval \(0.6371\) (lower bound) to \(0.7257\) (upper bound) is calculated. For part (b), when interpreting a confidence interval, we use the concept of where the true proportion is likely to be. Since it's a 95% confidence interval, we say that we are 95% confident.

Answer:

The proportion of all Canadians who support strict environmental controls on the Oil and Gas Industry is 95% confident to be somewhere between \(63.71\%\) (lower bound \(0.6371\times100 = 63.71\%\)) and \(72.57\%\) (upper bound \(0.7257\times 100=72.57\%\)).