Cyber Monday Shopping A survey of 1000 U.S. adults found that 33 % of people said that they woul

step 1 Kedok, let's calculate some confidence intervals today. We're given a total population of 1 ,000

Cyber Monday Shopping A survey of 1000 U.S. adults found...

Cyber Monday Shopping A survey of $1000 \mathrm{U.S}$.
adults found that $33 \%$ of people said that they would get
no work done on Cyber Monday since they would spend
all day shopping online. Find the $95 \%$ confidence inter-
val of the true proportion.

Key Concepts

Standard Error for Proportions

The standard error for proportions measures the variability of a sample proportion from sample to sample. It is calculated using the formula ?[p?(1 - p?)/n], where p? is the sample proportion and n is the sample size. This metric is crucial in determining the width of the confidence interval, as it quantifies how much the sample proportion is expected to fluctuate due to random sampling.

Critical Value (z-score)

The critical value, often derived from the standard normal distribution, represents the number of standard errors a point estimate must be from the true parameter to achieve a desired level of confidence. For a 95% confidence level, the critical value is typically about 1.96. This value is used to calculate the margin of error, which is then added to and subtracted from the point estimate to form the confidence interval.

Confidence Interval

A confidence interval is a range of values, calculated from sample data, that is likely to contain the true value of an unknown population parameter. In statistics, it provides an estimated interval which is likely to include the parameter of interest based on a chosen level of confidence, such as 95%. This interval quantifies the uncertainty inherent in using sample data to estimate a population characteristic.

Point Estimate of Proportion

The point estimate of a proportion is the observed fraction or percentage from the sample that represents the estimate of the true population proportion. It serves as the best single estimate for the population parameter and is used as the center of the confidence interval. For example, if a survey finds that 33% of respondents share a certain characteristic, this 33% is the point estimate of the true proportion in the population.

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