Concept of Student's T Probabilities

Student's t Distribution:

Whenever the population standard deviation is not known, the mean consists of a Student's t-distribution. The Student's t distribution was made by an Irish brewery worker William T. Gosset. The brewery wouldn't permit him to publish his work beneath his name; therefore he used the pseudonym ‘Student’.

The Student's t-distribution is much similar to standard normal distribution.

a) It is symmetric on its mean.

b) It consists of a mean of zero.

c) It consists of a standard deviation and variance more than 1.

d) There are really many t-distributions, one for each degree of freedom.

e) Since the sample size rises, the t distribution approaches to the normal distribution.

f) This is bell shaped.

g) The t-scores can be positive or negative; however the probabilities are always positive.

Degrees of Freedom:

It is a degree of freedom which takes place for every data value that is permitted to differ once a statistic has been fixed. For single mean, there are (n-1) degrees of freedom. This value will modify depending on the statistic being employed.

Population Standard Deviation Unknown:

When the population standard deviation, sigma is not known, then the mean consists of a student's t-distribution and the sample standard deviation is utilized rather than the population standard deviation.

The maximum error of estimate is provided by the formula for E as shown below. ‘t’ here is the t-score obtained from the Student's t-table. t-score is a factor of the level of confidence and sample size.

E = tα/2 (s/√n)

Once you have calculated E, now it is recommended to save it to the memory on your calculator. On TI-82, an excellent choice would be the letter E. The reason for this is that the limits for confidence interval are now found by adding up and subtracting the maximum error of estimate from or to sample mean.


Note that the formula is similar as for population mean when the population standard deviation is known. The only thing that has modified is the formula for maximum error of the estimate.

Latest technology based Statistics Online Tutoring Assistance

Tutors, at the, take pledge to provide full satisfaction and assurance in Statistics help via online tutoring. Students are getting 100% satisfaction by online tutors across the globe. Here you can get homework help for Statistics, project ideas and tutorials. We provide email based Statistics help. You can join us to ask queries 24x7 with live, experienced and qualified online tutors specialized in Statistics. Through Online Tutoring, you would be able to complete your homework or assignments at your home. Tutors at the TutorsGlobe are committed to provide the best quality online tutoring assistance for Statistics Homework help and assignment help services. They use their experience, as they have solved thousands of the Statistics assignments, which may help you to solve your complex issues of Statistics. TutorsGlobe assure for the best quality compliance to your homework. Compromise with quality is not in our dictionary. If we feel that we are not able to provide the homework help as per the deadline or given instruction by the student, we refund the money of the student without any delay.