How are statistics and empirical probablity related? What is a specific scientific decision?
Statistics is a mathematical method of determining trends and deviations from trends via probabilities. Essentially no results are absolutely certain, there is always a probability of alpha or beta errors. However, from the data, you can make a specific decision to accept or reject the null hypothesis.
This should give you a start. Thanks for asking.
give the exact and approximate solution to three decimals places x^2+2x+1=36
Statistics and empirical probability are closely related in the field of data analysis and inference.
Statistics is a branch of mathematics that involves collecting, analyzing, interpreting, and presenting data. It provides methods and tools to describe and summarize data, make inferences about populations based on sample data, and quantify the uncertainty associated with these inferences.
Empirical probability, on the other hand, refers to the probability based on observed data or empirical evidence. It is computed by counting the number of times an event of interest occurs relative to the total number of observations. Empirical probability relies on the assumption that the observed data is representative of the underlying probability distribution.
The relationship between statistics and empirical probability can be understood in the context of hypothesis testing, a common scientific decision-making process. In hypothesis testing, statisticians use sample data to make inferences about population parameters. These inferences are based on the concept of statistical significance, which quantifies the probability of obtaining the observed data if the null hypothesis (a specific scientific statement to be tested) is true.
To make a specific scientific decision using statistics and empirical probability, one typically follows these steps:
1. Formulate the hypothesis: Clearly define the null hypothesis (H0), which states that there is no significant effect or relationship, and the alternative hypothesis (Ha), which represents the desired outcome or the presence of an effect.
2. Collect and analyze data: Gather relevant data through observation, experiments, or surveys. Analyze the collected data using appropriate statistical techniques, such as descriptive statistics or inferential analysis.
3. Determine the test statistic: Based on the hypothesis and data, calculate an appropriate test statistic (e.g., t-test, chi-square test, etc.) that measures the degree of support for or against the null hypothesis.
4. Set the significance level: Determine the level of significance (alpha) for the test, which represents the maximum probability of rejecting the null hypothesis when it is true. Commonly used significance levels are 0.05 (5%) or 0.01 (1%).
5. Compute the p-value: The p-value is the probability of obtaining a test statistic as extreme as the one observed, assuming that the null hypothesis is true. It quantifies the evidence against the null hypothesis.
6. Make a decision: Compare the p-value to the significance level. If the p-value is smaller than the chosen significance level, reject the null hypothesis and accept the alternative hypothesis. Otherwise, fail to reject the null hypothesis.
7. Draw conclusions: Based on the decision made in step 6, interpret the results and draw conclusions about the presence or absence of the hypothesized effect or relationship.
In summary, statistics provides the framework and tools to analyze data and make scientific decisions, while empirical probability is used to estimate probabilities based on observed data. The combination of these two concepts allows researchers to draw valid conclusions and make informed decisions in various scientific disciplines.