Question

The city of Raleigh has 11700 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 250 randomly selected registered voters was conducted. 77 said they'd vote for Brown, 160 said they'd vote for Feliz, and 13 were undecided.

Give the sample statistic for the proportion of voters surveyed who said they'd vote for Brown. Note: The proportion should be a fraction or decimal, not a percent. This sample statistic suggests that we might expect of the 11700 registered voters to vote for Brown.

Answer 1

The sample statistic for the proportion of voters surveyed who said they'd vote for Brown is 0.308.

The expected numbers of voters who would vote for Brown is 3604.

Explanation:

The sample statistic is a numerical quantity used to represent a characteristic of a sample. For example, sample mean is a sample statistic representing the average of the sample. Or, sample proportion is a sample statistic representing the proportion of a particular variable in the sample. Or sample variance is a sample statistic representing the variance of the sample.

The sample statistic can be used to estimate the population parameter.

They are known as the point estimate of the parameter.

The sample proportion of a variable X is given by:

`\hat p=(X)/(n)`

It is provided that of the n = 250 registered voters selected, the number of voters who said they would vote for Brown is X = 77.

Compute the sample statistic for the proportion of voters surveyed who said they'd vote for Brown as follows:

`\hat p=(X)/(n)`

`=(77)/(250)\\`

`=0.308`

Thus, the sample statistic for the proportion of voters surveyed who said they'd vote for Brown is 0.308.

Compute the expected number of people of the 11700 registered voters who would vote for Brown as follows:

`E(X)=N* \hat p`

`=11700* 0.308\\=3603.6\\\approx 3604`

Thus, the expected numbers of voters who would vote for Brown is 3604.