The p hat is an abbreviation for sample proportion. It’s written as a lower-case p with a little caret above it in equations.
The difference between a population and a sample must first be grasped in order to understand what the phat symbol signifies and how it is utilised. The term “population” is used in statistics to refer to the entire group being researched. On the other hand, a “sample” is a subset of that group. A sample should ideally be typical of the full group, allowing statisticians to investigate the habits, behaviours, and features of that small group before extrapolating the results to the entire population. A lower-case p without a caret above it stands for “population proportion” in statistics. The entire group is taken into account when a statistician estimates the population proportion.
The p hat symbol, on the other hand, refers to a much smaller group: a percentage of the total group’s sample. When discussing survey results, the p hat is frequently utilised. A statistician, for example, asks 500 persons if they prefer grape soda; 342 say yes, 100 say no, and 58 say they don’t know. The statistician is curious about which proportion of people prefer grape soda, thus an equation will be devised to get the phat, or the proportion of people who said yes. The percentage or fraction of the sample group will then be calculated.