Question

an environmentalist wishes to survey canadians to determine what percentage support strict environmental controls on the oil and gas indus
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 ( =)
upper bound ( =)
(b) interpret the meaning of the interval you found in part (a).
who support strict environmental controls on the oil and gas industry is
decimals.)
the proportion of all canadians
the proportion of all canadians sampled
all people
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Explanation:

Step1: Calculate the sample proportion

The sample proportion $\hat{p}=\frac{x}{n}$, where $x = 484$ and $n=700$.
$\hat{p}=\frac{484}{700}\approx0.6914$

Step2: Calculate the standard error

The standard error $SE=\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}$.
Substitute $\hat{p}=0.6914$ and $n = 700$:
$SE=\sqrt{\frac{0.6914\times(1 - 0.6914)}{700}}=\sqrt{\frac{0.6914\times0.3086}{700}}\approx\sqrt{\frac{0.2134}{700}}\approx\sqrt{0.000305}\approx0.0175$

Step3: Find the z - value for 95% confidence interval

For a 95% confidence interval, the z - value $z = 1.96$

Step4: Calculate the lower and upper bounds

The lower bound $LB=\hat{p}-z\times SE$
$LB=0.6914-1.96\times0.0175=0.6914 - 0.0343=0.6571$

The upper bound $UB=\hat{p}+z\times SE$
$UB=0.6914+1.96\times0.0175=0.6914 + 0.0343=0.7257$

A confidence interval for a proportion gives a range of values within which the True population proportion is likely to lie. In this case, the 95% confidence interval for the proportion of Canadians who support strict environmental controls on the Oil and Gas Industry is calculated. The formula for the confidence interval for a proportion is $\hat{p}\pm z\times\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}$, where $\hat{p}$ is the sample proportion, $z$ is the z - value corresponding to the desired confidence level (for 95% confidence, $z = 1.96$), and $n$ is the sample size.

Answer:

Lower Bound = $0.6571$
Upper Bound = $0.7257$