ESTIMATION

• • Population Mean (M): Denoted by μ, it represents the average value of the entire population.
  • Population Variance (σ²): Denoted by σ², it measures the spread or variability of data points in the entire population.
  • Population Standard Deviation (σ): Denoted by σ, it is the square root of the variance and provides a measure of how much individual data points deviate from the mean.
  • Observation(N): Each data point in the population contributes to these measures.
• • Sample is a subset of the population that we actually observe or collect data from.
  • When dealing with a sample, we use the following symbols:
  • Sample Mean (x̅): Denoted by x̅ (pronounced as “X-bar”), it represents the average value of the sample.
  • Sample Variance (s²): Denoted by s², it measures the spread of data points within the sample.
  • Sample Standard Deviation (s): Denoted by s, it is the square root of the sample variance.
  • Observation(n): Each data point in the sample contributes to these measures.
• confidence level 99 % or 0.99 / critical value 2.58
• confidence level 95 % or 0.95/ critical value 1.96
• confidence level 90% or 0.90 / critical value 1.645
• • The confidence level determines the critical value to use in the formula.
  • The higher the confidence level, the larger the critical value and thus the wider the confidence interval.
  • Critical values define regions in the sampling distribution of a test statistic.
  • In hypothesis tests, critical values determine whether the results are statistically significant.
• •  point estimate is a single value that serves as an estimate for a population parameter based on sample data.
  • For instance, if we calculate the sample mean (average) from a dataset, that value represents a point estimate of the population mean.
  • Point estimates are straightforward to compute and provide a quick snapshot of the parameter.
• • interval estimate provides a range of values within which the population parameter is expected to lie.
  • The most common type of interval estimate is the confidence interval.
  • A confidence interval gives us both an upper and lower bound, indicating the plausible range for the parameter.
  • For example, if we calculate a 95% confidence interval for the population mean, it might look like: “The true population mean lies between X and Y.”
  • Interval estimates are more robust because they account for variability and uncertainty in the data.