Question

Consider a coin. Suppose you want to learn about the distribution of flips of the coin that land on Heads but you only want to flip the coin 20 times.

Suppose you flip a coin 20 times and record the count and proportion of times it lands on Heads.

1. Is the proportion of Heads among the 20 flips of the coin a parameter or a statistic? What symbol is used to denote the proportion?    

2. Is the proportion of Heads among all possible flips of the coin a parameter or a statistic? What symbol is used to denote the proportion?      

3. If we were to take several different samples of 20 flips of the coin, would all of the samples contain the same proportion of Heads?

Answer 1

1)Proportion of head among 20 flips estimates the actual proportion of heads in flips of coin distribution.Hence it is a statistic as it measures estimate of population proportion based on sample.

Sample proportion is denoted by

2)proportion of Heads among all possible flips of the coin is a parameter as it is a population based value.

Population proportion is denoted by p.

3)If we were to take several different samples of 20 flips of the coin, not all of the samples contain the same proportion of Heads, since different samples can have different amounts of heads in set of 20 flips per sample. Some may have more heads in 20 flips, some may have less heads

thus resulting in varying sampling results of sample proportion

If there is any understanding problem regarding this please feel free to ask any doubt in comment box.