Construct the appropriate confidence interval. A simple...

Construct the appropriate confidence interval. A simple random sample of size $n=300$ individuals who are currently employed is asked if they work at home at least once per week. Of the 300 employed individuals surveyed, 35 responded that they did work at home at least once per week. Construct a $99 \%$ confidence interval about the population proportion of employed individuals who work at home at least once per week.

Construct the appropriate confidence interval.
A simple random sample of size $n=300$ individuals who are currently employed is asked if they work at home at least once per week. Of the 300 employed individuals surveyed, 35 responded that they did work at home at least once per week. Construct a $99 \%$ confidence interval about the population proportion of employed individuals who work at home at least once per week.

Key Concepts

Confidence Interval

A confidence interval is a range of values, derived from sample data, that is likely to contain the true value of an unknown population parameter. It is constructed to reflect the level of confidence that the interval includes the parameter, based on the sampling variability and chosen confidence level.

Sample Proportion

The sample proportion is the ratio of the number of successes (or the count of interest) to the total number of observations in the sample. It serves as an estimator for the true population proportion and forms the basis for further inferential statistics.

Standard Error

The standard error quantifies the variability of the sample proportion due to random sampling. It is calculated using the estimated proportion and the sample size, providing a measure of how much the sample proportion is expected to deviate from the true population proportion.

Critical Value (Z-Score)

The critical value, often obtained from the standard normal distribution, represents the number of standard deviations needed to achieve a specified confidence level in a two-tailed test. It is essential in determining the extent of the margin of error in a confidence interval.

Margin of Error

The margin of error defines the maximum expected difference between the true population parameter and the sample estimate. It is computed by multiplying the critical value with the standard error, thereby determining the range within which the population parameter is expected to lie.

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