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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 0.03 of the true proportion?



Answer :

At least 99% confidence that the sample percentage is inside 0.03 of the absolute proportion is required for 1844 residents.

Choose p = 0.5 since the previous estimate of population percentage is uncertain.

E = 0.03 is the margin of error.

A 99% confidence interval requires the following crucial value: [tex]z_{a/2}[/tex] = 2.576

The act of deciding how many observations or repetitions to incorporate into a statistical sample is known as sample size determination.

The sample size,

n = 0.5 × (1 - 0.5) × ([tex]z_{a/2}[/tex] ÷ E)²

n = 0.25 × (2.576 ÷ 0.03)²

n = 1843.27 ≈ 1844

As a result, the needed sample size is 1844.

Read more about the sample proportion of confidence interval at

https://brainly.com/question/18485135?referrer=searchResults

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