Question

The Arizona Department of Transportation wishes to survey state residents to determine what proportion of the population would like to increase statewide highway speed to 75 from 65 mph. At least how many residents do they need to survey if they want to be at least 99% confident that the sample proportion is within 0.05 of the true proportion

Answer 1

The answer is "6.635776".

Explanation:

If the proportion estimation is not given, then the approximate is true. So, it is in the top condition, which referring its overall error margin that is equal to 0.5.

Therefore the margin of error=0.05 With z=2.576

`\to 0.05=2.576 * \sqrt{(0.05 * (0.05)/(N))}\\\\\to 0.05=2.576 * \sqrt{( (0.0025)/(N))}\\\\\to √(N)= (2.576 * 0.05)/(0.05)\\\\\to √(N)= 2.576`

square the above equation:

`\to (N)^2= (2.576)^2\\\\\to N^2= 6.635776\\\\`

So the number of required residents=6.635776