What is population? The 200 students of small college with size N=200 is the population.
What is the variable? The amount of financial aid received by individual student at the college is (quantitative) variable (say X).
What is the population mean? The mean amount of financial aid
received of $1500 by the students at the college is the population
mean. It is denoted by:
Formulae:
Sample size (n)=total number of observations/values in the sample. Here, n=8.
xi denote sample observations.
Sample mean= sum of all the values of variable present in the sample divided by the sample size.
Sample standard deviation is the square root of sample variance which is computed by-
Student's t-statistic that follows t-distribution with n-1 degrees of freedom is given by-
Null Hypotheisis | H0: |
Alternative Hypothesis | H1: |
TABLE | Random sample 1 | Random sample 2 | Random sample 3 | ||
Sample Means | |||||
Sample standard deviation |
|
|
984.7951 | ||
absolute value of student t-statistic |
|
|
2.18286 | ||
tabulated value for t at 5% level of significance | 2.37 | 2.37 | 2.37 | ||
Result | Accept H0 | Accept H0 | Accept H0 |
No, all three samples do not have the same means.
No, all samples do not give good estimates of population mean if we just observe the sample means in the table above. But by procedure if we carry out t-test for single mean, the result completely alters; we accept H0 in each case which means they give good estimates. This is due to small sample size, 8.
Population mean () is the parameter
whereas sample mean (
) is the
statistic. Sample standard deviation is also statistic.
Population mean, population standard deviation, population proportion are all parameters.
Sample mean, sample standard deviation, sample proportion, student's t-statistic (used for testing of hypothesis) are all statistic.
Completed table using the statistics symbols is as follows:
Population (Parameter) | Sample (Statistic) | |
Proportion | p | |
Mean | ||
Standard Deviation |
Note that symbols may (or may not) change according to domain of application of statistics. Sometimes, all capital letters are used for population "parameter" and small letters for sample "statistic".
Question: How accurate are random samples at prediction this population proportion of 0.607 Consi...
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