When constructing a sample, make sure to use random sampling and consider properties like representativeness and independence of observations. For samples of size 2, select elements independently and at random from the population. The number of different samples of size n can be calculated using the combination formula. As the sample size increases, the shape of the data distribution becomes more symmetrical and bell-shaped.
When constructing a sample of size n, it is important to use random sampling to ensure that each element in the population has an equal chance of being selected. The properties of a sample include representativeness, where the sample accurately represents the population, and the independence of observations, where each observation in the sample is independent of one another.
For random vector sampling with samples of size 2, the construction involves selecting two elements independently and at random from the population. This can be done by using techniques such as drawing names from a hat or using a random number generator.
The number of different samples of size n that can be obtained from k elements of E can be calculated using the combination formula, which is given by C(k, n) = k! / ((k-n)! * n!). This formula calculates the number of ways to choose n elements out of k distinct elements, without regard to the order in which they are chosen.
The change in sample size (n) can affect the shape of the distribution of the data. As n increases, the sampling distribution of the mean approaches a normal distribution. This means that the data becomes more symmetrical and bell-shaped.