Question

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Q1:What is the difference between a population and a sample in statistics? (in details) (((use your own words.))))

Q2. How to interpret confidence intervals and confidence levels?(in details) (((use your own words.))))
Q3. Why the p-value is important?(in details) (((use your own words.))))

Answer 1

Answer1:

In statistics, population is an aggregate of facts or figures under study. For example, if we study the average salary of an employee in a firm, then the salaries of all the employees in the firm, will costitute a population. A population may be either finite or infinite. In a finite population, the number of elements is finite. For example, all the students in a college in the current session. In an infinite population, the number of elements is infinite. For example, the stars in the universe. Population characteristics like population mean, population variance etc are called parameters. The value of a parameter is always a constant. The advantages of population study are getting more accuracy, detaied information about the population. The disadvantages of the population study are expensive, time consuming and getting more labour, more skilled personnels.

In statistics, a sample is a part of a well defined population. For example, if we study the average height of a person in the age group 20 to 25 years in your country, which is not feasible, in this case we can take few persons in your locality and then find the average of them. Then the the persons that we consider in your locality, will constitute a sample. A sample is always finite. The sample characteristics like sample mean, sample variance etc. are called statistics. The value of a statistic is not a constant, it varies sample to sample. The advantages of sample study are less cost. requirement of less labour, more reliable and getting more information. The disadvantages are more skilled personnels required, less detailed information etc.

Answer2:

Let, be a parameter, which is unknown. Let, be the corresponding statistic. If and be the values of the statistic , such that . Then and are called confidene interval of the parameter . is called level of significance and is called confidence level of coefficient of confidence. The values of the confidence intervals and vary with the change of the value of level of significance. Generally, the width - increases with decrease in the value i.e. the increase in the value of cofidence level . A good condfidence interval is that whose width    - is minimun at the certain level of significance .

Answer3

p value is the area of the normal curve which lies at the right of the vlue of the statistic Z (say). In ther words, if 'a' is the value of the test statistic Z, then Pr[ Z > a] = p. In testing of hypothesis, if the p vale , the level of significance, the null hypothesis H0 is not rejected , otherwise H0 is rejected.