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Standard error is a crucial concept in statistics that measures the variability of a sample proportion. It helps to understand how much a sample statistic is expected to fluctuate when you take different samples from the same population. To calculate the standard error for a population proportion, we use the formula:
\[ \text{SE} = \sqrt{\frac{p(1-p)}{n}} \]where:

• \( p \) is the sample proportion (71% or 0.71 in this problem)
• \( n \) is the sample size (900 in this problem)

Plug these values into the formula to find the standard error. The smaller the standard error, the more reliable your sample mean (or proportion) is as an estimate of the population mean (or proportion). A smaller SE means the sample data are tightly clustered, making the mean an accurate representation of the population.

The Z-score is a statistical measurement that describes a value's relation to the mean of a group of values. When we calculate a confidence interval, we use the Z-score to determine how confident we are in our estimate. In particular, the Z-score helps us set the boundaries of our confidence interval.
In the given exercise, we want a 99% confidence level, which is quite high. A 99% confidence level ties to a Z-score of approximately 2.57. To find this, one would typically refer to the standard normal distribution table or use statistical software. This Z-score value suggests that our sample proportion is 2.57 standard errors away from the true population proportion.
The higher the confidence level, the larger the Z-score, and consequently, the wider the confidence interval. This statistical concept ensures that your estimate is less likely to miss the population parameter even if it results in a larger range.

Population proportion is a fundamental statistic that represents the fraction of individuals in a population possessing a particular attribute. In this problem, the population proportion refers to the percentage of Californians who support the 10-2 verdict.
The sample proportion of 71% (or 0.71) is our best estimate of the true population proportion in this case. It's important to note that we use the sample proportion to make inferences about the entire population, which is seldom observed directly due to time and cost constraints.

• The confidence interval assists in determining an estimated range in which the true population proportion is likely to fall.
• By calculating the confidence interval, we specify a certain level of confidence (in this case, 99%) that the interval computed from the sample data contains the population parameter.

Understanding population proportion helps us gauge public opinion or behavior across different demographics and it plays a key role in statistical studies and surveys.