Means

At least one student in the population spends between 8 and 12 hours studying.

Every student in this high school spends between 8 and 12 hours studying on average.

We are 95% confident that the true population mean falls between 8 and 12 hours.

The true population mean must be exactly 10 hours because it's the midpoint of the interval.

Every individual has an equal chance of being selected.

Individuals are selected based on convenience.

Individuals are chosen from pre-determined starting points.

Subgroups in the population each have an equal representation in the sample.

The estimate is more accurate

The sample size is large

The sample size is small

The estimate is less accurate

There are more observations in the sample than initially planned during study design.

Data collection methods lead to precise measurements with little variation.

The sample variance is less than the actual population variance due to random sampling variation.

An outlier has been removed from the dataset, increasing precision in estimating parameters.

Stratified Random Sampling

Cluster Sampling

Convenience Sampling

Systematic Sampling

Z-interval based on known standard deviation and known population variance

Bootstrap method for constructing non-parametric confidence intervals

Chi-squared interval using estimated sample variance to estimate population standard deviation

T-interval with unknown population variances and assumed sample standard deviation

Range

Outliers

Mean

Quartiles

Increasing sample size decreases both variability and uncertainty, resulting in wider intervals.

Sample size has no impact on confidence intervals as they depend solely on standard deviation.

Larger sample sizes reduce variability in estimates, leading to more precise intervals.

Smaller samples tend to have less variability which increases certainty about where the true mean lies.

To determine if there is a significant difference between two population means.

To predict individual outcomes based on sample data.

To calculate the probability that a sample mean is equal to the population mean.

To estimate the range within which the true population mean lies with 95% certainty.

Simple random sampling

Stratified random sampling

Systematic sampling

Cluster sampling