 # Two individuals are running for mayor of your town. You conduct an election survey a week before the election and find that 51% of the respondents prefer candidate A. Can you predict a winner? Use the 99% level. ( HINT: In a two-candidate race, what percentage of the vote would the winner need? Does the confidence interval indicate that candidate A has a sure margin of victory? Remember that while the population parameter is probably [ α = 0.01 ]in the confidence interval, it may be anywhere in the interval .) P s = 0.51 N = 578 ### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836 ### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

#### Solutions

Chapter
Section
Chapter 6, Problem 6.15P
Textbook Problem
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## Two individuals are running for mayor of your town. You conduct an election survey a week before the election and find that 51% of the respondents prefer candidate A. Can you predict a winner? Use the 99% level. (HINT: In a two-candidate race, what percentage of the vote would the winner need? Does the confidence interval indicate that candidate A has a sure margin of victory? Remember that while the population parameter is probably [ α = 0.01 ]in the confidence interval, it may be anywhere in the interval.) P s = 0.51 N = 578

Expert Solution
To determine

To find:

The confidence interval for the population mean for the specified level.

### Explanation of Solution

Given:

The given information is,

Two individuals are running for mayor of your town. You conduct an election survey a week before the election and find that 51% of the respondents prefer candidate A.

The sample proportion is 0.51, population proportion is 0.5 and sample size is 578.

Approach:

The confidence interval is an interval estimate from the statistics of the observed data that might contain the true value of the unknown population parameter.

Formula used:

For large samples and given sample proportion, the confidence interval (c.i.) is given by,

c.i.=Ps±Z(Pu(1Pu)N)

Where, Ps is the sample proportion,

Pu is the population proportion,

Z is the Z score determined by the alpha level and,

N is the sample size.

Calculation:

The population proportion is 0.5, sample proportion is 0.51.

For 99%, the Z value is given as,

Z(99%)=2.58

For large samples and given sample proportion, the confidence interval (c.i.) is given by,

c

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