Final answer:
The statement is false; a smaller sample size usually leads to faster report generation but may result in less accurate and reliable data. Larger sample sizes decrease the error bound and provide narrower confidence intervals, which correspond to more precise estimates.
Step-by-step explanation:
The statement is false; decreasing the sample size for a report does not mean that more sessions will be used to calculate the report and it will take longer to generate. In fact, a smaller sample size generally means that there is less data to process, potentially speeding up the calculation time. However, it is important to consider the quality and reliability of the report. As mentioned, larger sample sizes are generally better than smaller ones in scientific experiments because they tend to reduce sampling variability and provide more precise estimates, leading to more reliable statistics.
Larger sample sizes allow the application of the central limit theorem, which states that the sampling distribution of the means will be approximately normal, regardless of the population's distribution, given a large enough sample size. Moreover, having a larger sample size decreases the error bound and makes the confidence interval narrower, giving more accurate results.
Conversely, decreasing the sample size leads to an increase in the error bound and thus a wider confidence interval, indicating more uncertainty in the estimate. This increased variability may sometimes require a larger interval to capture the true population mean, particularly when working with smaller samples.