Explain what precision and confidence are and how they influence samplesize.

Precision and confidence are two important concepts in statistics, particularly in the context of sample size determination.

1. Precision: Precision refers to how close the estimates from different samples are to each other. In other words, it's a measure of the variability or dispersion of the sampling distribution. The smaller the variability (i.e., the higher the precision), the closer the sample estimates are to the true population parameter. Precision is usually specified in terms of a margin of error. A smaller margin of error indicates higher precision.

2. Confidence: Confidence, on the other hand, refers to how certain we are that the true population parameter lies within a certain range. This range is usually specified as a confidence interval. A higher confidence level means we are more certain that the true population parameter lies within the specified range.

3. Influence on Sample Size: Both precision and confidence level influence the sample size. If we want higher precision (i.e., a smaller margin of error), we need a larger sample size. This is because a larger sample size reduces the variability of the estimates, leading to higher precision. Similarly, if we want a higher confidence level (i.e., we want to be more certain that the true population parameter lies within a certain range), we also need a larger sample size. This is because a larger sample size reduces the likelihood of extreme sample estimates, making us more confident that the true population parameter lies within the specified range.

In summary, both precision and confidence level are directly related to sample size: the higher the desired precision or confidence level, the larger the required sample size.