8.22 Fear Factor In a survey of 1275 Canadians aged 18 and over conducted by EKOS...

8.22 Fear Factor

In a survey of 1275 Canadians aged 18 and over conducted by EKOS Research, 69% of Canadians said they thought the world is more dangerous today than it was 25 years ago. a. Find a point estimate for the proportion of Canadian adults who fear that the world is more dangerous today than it was 25 years ago. Calculate the margin of error. b. The poll reports a margin of error of plus or minus 2.7%. Does this agree with your results in part a? If not, what value of p produces the margin of error given in the poll?

Significance Level : 5%, alpha = .05

Find a point estimate for the proportion of Canadian adults who fear that the world is more dangerous today than it was 25 years ago. Calculate the margin of error.
The poll reports a margin of error of plus or minus 2.7%. Does this agree with your results in part a? If not, what value of p produces the margin of error given in the poll?

Solutions

Expert Solution

(a) The point estimate = 0.69

Margin of Error. ME

Therefore ME = 2.54%

(b) No, the value of ME as per = 0.69 is 2.54%

To have an ME of 2.7% = 0.027

Squaring and solving

Therefore (0.027 1.96)² * 1275/ = * (1 - )

Therefore - ² = 0.242

² - + 0.242 = 0

Solving for , we get = 0.5898 0.59

__________________________________________

To solve for , we use the equation to find the roots

Here a = 1, b = -1 and c = 0.242. Substituting in the above equation gives the value of .

orchestra answered 1 year ago

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