Question

1.1 estimating populations: problem 4. (1 point) the city of raleigh has 9600 registered voters. there are two candidates for city council in an upcoming election: brown and feliz. the day before the election, a telephone poll of 380 randomly selected registered voters was conducted. 115 said theyd vote for brown, 233 said theyd vote for feliz, and 32 were undecided. (a) what is the size of the population? 9600 voters (b) what is the size of the sample? 380 voters (c) give the sample statistic as a percentage for the proportion of voters surveyed who said theyd vote for brown. round your answer to at least 2 decimal places. for example 12.59345 rounded to 2 decimal places is 12.59. % (d) based on this sample, what is the total number of voters we might expect to vote for brown? round your answer down to the nearest integer. for example 223.687 rounds down to 223. voters

Explanation:

Step1: Calculate proportion for Brown

The proportion of voters who said they'd vote for Brown in the sample is $\frac{115}{380}$.

Step2: Convert to percentage

To convert the proportion to a percentage, we multiply by 100: $\frac{115}{380}\times100=\frac{11500}{380}\approx 30.26\%$.

Step3: Estimate total voters for Brown

We use the proportion from the sample to estimate the number of voters for Brown in the whole population. Let $x$ be the number of voters for Brown in the population. We set up the proportion $\frac{115}{380}=\frac{x}{9600}$. Cross - multiplying gives $380x = 115\times9600$. Then $x=\frac{115\times9600}{380}=\frac{1104000}{380}\approx 2905.26$. Rounding down, we get 2905.

Answer:

(c) 30.26%
(d) 2905 voters