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In statistics, **sample size** refers to the number of observations or data points collected in a study. For example, in the given exercise, the sample size is 15. Sample size is a crucial concept because it impacts the accuracy and reliability of the statistical results. A larger sample size generally provides a more accurate estimate of the population parameters.

Sample size also plays a role in the application of the Central Limit Theorem (CLT). According to the CLT, if the sample size is large enough (typically n > 30), the distribution of the sample means will be approximately normal, regardless of the shape of the population distribution. However, when the population is already normally distributed, even a smaller sample size (like 15) will result in sample means that are normally distributed.

A **normal distribution** is a bell-shaped distribution that is symmetrical around its mean. It is one of the most important probability distributions in statistics because many real-world phenomena follow this pattern. In the context of the given exercise, the weights of golden retriever dogs are said to be normally distributed in the population.

A normal distribution is characterized by its mean and standard deviation. The mean determines the center of the distribution, while the standard deviation indicates how spread out the values are around the mean. Because the original population of dog weights is normally distributed, the sample means will also follow a normal distribution, thanks to the Central Limit Theorem (CLT).

**Statistical inference** involves making conclusions about a population based on a sample. It includes various techniques that allow researchers to make predictions or generalizations from data. For example, in the exercise, we make an inference about the distribution of the sample means based on the known population distribution.

There are two main types of statistical inference: estimation and hypothesis testing. Estimation involves estimating population parameters (like the mean or standard deviation) from the sample data. Hypothesis testing is used to test an assumption or claim about a population. The Central Limit Theorem (CLT) aids statistical inference by allowing us to assume that sample means will follow a normal distribution, making it easier to estimate population parameters and test hypotheses.

**Population distribution** describes how the values of a variable are distributed in a whole population. It provides a complete picture of how individual data points are spread across different values. In the exercise, the population distribution of golden retriever weights is given as normal.

Understanding the population distribution is crucial because it helps in choosing the appropriate statistical methods for data analysis. If the population distribution is normal, as in this case, the sample means can be treated as normally distributed even with smaller sample sizes. This is a significant point from the Central Limit Theorem (CLT) which states that the sampling distribution of the sample mean will be normal if the original population is normal, regardless of sample size.