Glossary
Claim (in testing)
A specific hypothesized value for a population parameter that is evaluated using statistical evidence.
Example:
A company made the claim that 80% of their customers are satisfied, which we then tested with a confidence interval.
Confidence Interval
A range of values, calculated from sample data, that is likely to contain the true population parameter.
Example:
After surveying students, we found a 95% confidence interval for the proportion who prefer online classes to be (0.55, 0.65).
Confidence Level
The probability that a randomly constructed confidence interval will contain the true population parameter.
Example:
A 99% confidence level means that if we repeated the sampling process many times, 99% of the resulting intervals would capture the true parameter.
Context (in interpretation)
The specific real-world scenario or subject matter to which the statistical findings are applied and explained.
Example:
When interpreting a confidence interval, always include the context, such as 'the true proportion of students who prefer online learning'.
Critical Value (z*)
A multiplier from the standard normal distribution that determines the number of standard errors to extend from the point estimate to achieve a desired confidence level.
Example:
For a 95% confidence interval, the critical value (z*) is approximately 1.96.
Independent (condition)
A condition for inference requiring that individual observations in the sample are independent of each other, often checked by the 10% rule for sampling without replacement.
Example:
We checked the Independent condition by ensuring our sample of 50 students was less than 10% of the total student population.
Large Counts (condition)
A condition for inference for proportions requiring that the expected number of successes and failures in the sample are both at least 10.
Example:
To meet the Large Counts condition, we confirmed that both np ≥ 10 and n(1-p) ≥ 10, ensuring the sampling distribution is approximately normal.
Margin of Error (MOE)
The maximum expected difference between the sample estimate and the true population parameter, determining half the width of the confidence interval.
Example:
If our confidence interval is (0.60, 0.70), the margin of error is 0.05, meaning our estimate is likely within 5 percentage points of the true value.
Population Proportion
The true percentage of individuals in an entire population that possess a specific characteristic.
Example:
We want to estimate the population proportion of all high school students in the state who own a smartphone.
Random (condition)
A condition for inference requiring that the data come from a well-designed random sample or randomized experiment to ensure representativeness.
Example:
To satisfy the Random condition, the survey participants were selected using a simple random sample from the school's student roster.
Range of Values
The spread or interval within which a true population parameter is estimated to lie.
Example:
The range of values for our estimate of student satisfaction was from 70% to 80%.
Repeated Sampling Statement
An interpretation of a confidence interval that describes what would happen if the sampling process were repeated many times.
Example:
Our repeated sampling statement for a 95% CI would be: 'In repeated random sampling, approximately 95% of intervals created will capture the true population proportion'.
Sample Data
Information collected from a subset of a population, used to make inferences about the entire population.
Example:
We used sample data from 100 randomly selected voters to estimate the outcome of the election.
Sample Size (n)
The number of individuals or observations included in a statistical sample.
Example:
Increasing the sample size from 100 to 400 will make our confidence interval narrower, providing a more precise estimate.
Standard Error (SE)
An estimate of the standard deviation of a sample statistic's sampling distribution, indicating the typical distance a sample statistic falls from the true parameter.
Example:
The standard error for our sample proportion was calculated to be 0.02, indicating the typical variability of sample proportions around the true population proportion.
p-hat (sample proportion)
The proportion of successes observed in a sample, calculated as the number of successes divided by the sample size.
Example:
If 60 out of 100 surveyed students prefer online learning, then the p-hat is 0.60.