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.

Stratified Random Sampling

Cluster Sampling

Convenience Sampling

Systematic Sampling

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.

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.

Zero should be included in any valid interval regardless of the policy's effectiveness.

We are 95% confident that there is a nonzero change in mean temperature due to the new policy.

Omitting zeros suggests that the temperature changes are significantly higher than expected, not just non-zero.

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

It confirms that all future samples will also have means within this interval.

It indicates that there is no variation in the sampled data set.

It proves that this specific sample's mean is definitely equal to the population mean.

It suggests that this specific sample's mean is likely representative of the population mean.

Simple random sampling

Stratified random sampling

Systematic sampling

Cluster sampling