Final answer:
The best point estimate for 261 out of 300 people sampled is the Sample Mean. This is a statistic used to estimate the central tendency of a population. For hypothesis testing with a known population standard deviation and a large sample size, the Normal distribution is used, while the Student's t-distribution is used when the population standard deviation is unknown and the sample size is small.
Step-by-step explanation:
Out of 300 people sampled, 261 had the best point estimate for the Sample Mean. This scenario describes a statistical measurement that represents the central tendency of the sample data gathered from a population. The term 'best point estimate' indicates the most accurate estimation we can make for a certain population parameter based on the sample data.
Given the additional context about hypothesis testing and the distribution, when dealing with sample data and a known population standard deviation, typically a Normal distribution is used for the hypothesis testing. The central limit theorem supports this by stating that the distribution of the sample mean will approximate a normal distribution, especially with larger sample sizes.
When the population standard deviation is unknown and the sample size is small, the appropriate distribution for hypothesis testing is the Student's t-distribution. It deals with cases where we must estimate the population standard deviation using the sample standard deviation.