A local newspaper in a large city wants to assess support for the construction of a highway by-pass around the central business district to reduce downtown traffic. They survey a random sample of 1152 city residents and find that 543 of them support the bypass. The newspaper asks a statistician to construct a 99% confidence interval for the proportion of all city residents who support building the bypass. (A) State and provide verification that all conditions necessary for inference are satisfied (B) Show work needed to calculate the 99% confidence interval. (C) Interpret the confidence interval in context.

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Ogorwynego Ogorwynego · Answer 1

The confidence interval that is contained in the question shows that at 99% confidence, the interval falls between 0.43354, 0.5093

The sample size of the population is given as 1152

x = 543 that support the buy pas

We have to find the proportion

p = 543/1152

= 0.4714

α = 1 - 99%

= 0.01

α/2 = 0.01/2

= 0.005

Zα/2 = 2.5758

In order to calculate this you have to use the critical value calculator on excel

[tex]0.4714+-\frac{\sqrt{0.4714(1-0.4714)} }{1152}[/tex]

0.4714 ± √0.0002163

0.4714 ± 0.0147x2.5758

0.4714 ± 0.03786

0.43354, 0.5093

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