In a Gallup Poll, 44 % of the people polled answered "more...

In a Gallup Poll, $44 \%$ of the people polled answered "more strict" to the following question: "Do you feel that the laws covering the sale of firearms should be made more strict, less strict, or kept as they are now?" Suppose the margin of error in the poll was $3.5 \%$ and the estimate was made with $95 \%$ confidence. At least how many people were surveyed?

Key Concepts

Sample Proportion

The sample proportion is the fraction or percentage of the sample that exhibits a particular characteristic. It is used as an estimate for the true population proportion, and its variability is assessed using the standard error in the context of a confidence interval.

Critical Value

The critical value is a point on the standard normal distribution (or other relevant distributions) that corresponds to the desired confidence level. For instance, a 95% confidence interval typically uses a critical value of about 1.96, which is used to scale the estimate of the standard error.

Sample Size Determination

Sample size determination involves calculating the number of observations required so that the estimate of the population parameter falls within a specified margin of error at a given confidence level. For proportions, the formula involves the critical value, the sample proportion, and the desired margin of error to ensure the confidence interval is sufficiently narrow.

Margin of Error

The margin of error represents the range within which the true population parameter, such as a proportion, is estimated to lie with a certain level of confidence. It indicates how much the results obtained from the sample might differ from the true population value.

Confidence Level

The confidence level specifies the percentage of times that the true population parameter would lie within the estimated interval if the sampling were repeated numerous times. A 95% confidence level means that there is a 95% likelihood that the confidence interval contains the true parameter.

Transcript

Please give Ace some feedback