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Calculators and computers can easily calculate any Student's t-probabilities. The TI-83,83+, and 84+ have a tcdf function to find the probability for given values of t . The grammar for the tcdf command is tcdf(lower bound, upper bound, degrees of freedom). However for confidence intervals, we need to use inverse probability to find the value of t when we know the probability.

For the TI-84+ you can use the invT command on the DISTRibution menu. The invT command works similarly to the invnorm. The invT command requires two inputs: invT(area to the left, degrees of freedom) The output is the t-score that corresponds to the area we specified.

The TI-83 and 83+ do not have the invT command. (The TI-89 has an inverse T command.)

A probability table for the Student's t-distribution can also be used. The table gives t-scores that correspond to the confidence level (column) and degrees of freedom (row). (The TI-86 does not have an invT program or command, so if you are using that calculator, you need to use a probability table for the Student's t-Distribution.) When using a t -table, note that some tables are formatted to show the confidence level in the column headings, while the column headings in some tables may show only corresponding area in one or both tails.

A Student's t table (See [link] ) gives t -scores given the degrees of freedom and the right-tailed probability. The table is very limited. Calculators and computers can easily calculate any Student's t-probabilities.

    The notation for the Student's t-distribution (using T as the random variable) is:

  • T ~ t df where df = n – 1.
  • For example, if we have a sample of size n = 20 items, then we calculate the degrees of freedom as df = n - 1 = 20 - 1 = 19 and we write the distribution as T ~ t 19 .

If the population standard deviation is not known , the error bound for a population mean is:

  • E B M = ( t α 2 ) ( s n ) ,
  • t σ 2 is the t -score with area to the right equal to α 2 ,
  • use df = n – 1 degrees of freedom, and
  • s = sample standard deviation.

The format for the confidence interval is:
( x ¯ E B M , x ¯ + E B M ) .

To calculate the confidence interval directly:
Press STAT.
Arrow over to TESTS.
Arrow down to 8:TInterval and press ENTER (or just press 8).

Suppose you do a study of acupuncture to determine how effective it is in relieving pain. You measure sensory rates for 15 subjects with the results given. Use the sample data to construct a 95% confidence interval for the mean sensory rate for the population (assumed normal) from which you took the data.
The solution is shown step-by-step and by using the TI-83, 83+, or 84+ calculators.

  • 8.6
  • 9.4
  • 7.9
  • 6.8
  • 8.3
  • 7.3
  • 9.2
  • 9.6
  • 8.7
  • 11.4
  • 10.3
  • 5.4
  • 8.1
  • 5.5
  • 6.9

Press STAT and arrow over to TESTS .
Arrow down to 8:TInterval and press ENTER (or you can just press 8 ).
Arrow to Data and press ENTER .
Arrow down to List and enter the list name where you put the data.
There should be a 1 after Freq .
Arrow down to C-level and enter 0.95
Arrow down to Calculate and press ENTER .
The 95% confidence interval is (7.3006, 9.1527)


When calculating the error bound, a probability table for the Student's t-distribution can also be used to find the value of t . The table gives t -scores that correspond to the confidence level (column) and degrees of freedom (row); the t -score is found where the row and column intersect in the table.

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Questions & Answers

what percent of the students would be expected to score above 95?
Peachy Reply
inferential statistics is what?
Seyi Reply
in which we make infrences (hypothsis)
surpose a data set of 2,3,5,6,1,4 are given find median
lucy Reply
fastest finger please
Mean (average) 4... Median (middle term) 3.5.. Mode (frequency) every element in a set has 1 frequrncy
i arrange the data set in ascending order. that is, 1,2,3,4,5,6. then find the data set that falls in the middle. in this case, 3 & 4 fall in the middle. you then sum and obtain the average. that is, (3+4)/2=3.5. therefore, 3.5 is the median.
both of you are correct.
hello guys
great to be here
how does a line graph look
pls who knows how line graph look like
line graph usually have a straight line running through axis
am new here anyone willing to orient me?
find the media of the following numbers 61,64,67,70,73
lucy Reply
my body pls
what happen to your body@hana
what is the percentile for the set of data in the class C and frequency F(c,f)given by (9.3-9.7,2) (9.8-10.2,5) (10.3-10.7,12) (10.8-11.2,17) (11.3-11.7,14) (11.8-12.2,6) (12.3-12.7,3) (12.8-13.2,1)
Chinwendu Reply
how to find median
Hrishe Reply
arrange ascending and desending order than the mid value is Median
what if it is a group data
mean/ medium/ mode
n\2 and n+1\2
An operational manager at a manufacturing company is interested in the level of satisfaction of computer buyers. The manager has developed a satisfaction scale of 1-10 to mark their level of understanding with the company.What is the population of the interest?
thomas Reply
Any clues
how to use grouped and ungrouped data
Hassan Reply
Just a test from gplay
Lucy Reply
how come 5.67
Mano Reply
by dividing 11.37 on 2
by dividing 11.34 on 2
what is index number?
What is the differences between quota an lottery system of sampling
What are the are the characteristics that are critically expedients in selecting the sample size
fit a binomial distribution for the following data and test the goodness of fit x: 0 1 2 3 4 5 6 f: 5 18 28 12 7 6 4
Mikki Reply
solve the question please
can some please help solve so that we learn some
It is a square chi
But can't be a binomial because, the x numbers are 0 to 6, instead those would be "0" or "1" in a straight way
You can do a chi-square test, but the assumption has to be a normal distribution, and the last f's number need to be "64"
sorry the last f's numbers : "6 and 4" which are the observed values for 5 and 6 (expected values)
can't understand basic of statistics ..
Sorry I see my mistake, we have to calculate the expected values
So we need this equation: P= (X=x)=(n to x) p^x(1-p)^n-x
why it is not possible brother
were n= 2 ( binomial) x= number of makes (0 to 6) and p= probability, could be 0.8.
so after we calculate the expected values for each observed value (f) we do the chi-square. x^2=summatory(observed-expected)^2 / expected and compare with x^2 in table with 0.8
tomorrow I'll post the answer, I'm so tired today, sorry for my mistake in the first messages.
It is possible, sorry for my mistake
two trader shared investment and buoght Cattle.Mr.Omer bought 255 cows & rented the farm for a period of 32 days. Mr. Ahmed grazed his Cattle for 25 days. Mr. Ahmed's cattle was 180 cows.Together they profited $ 7800. the rent of the farm is $ 3000 so divide the profit per gows/day for grazing day
how to start this book, who is reading thins first time
Nissar Reply
It is my first time reading this book
Good one
from were did you get 2/50?m
Chico Reply
People living longer
Qader Reply
Why do you think that is?
because there is an increase in number of people with age more than 30.
Ok. And what do you think is the driving factor behind that hypothesis?
fewer birth and increase in # of years living or fewer dying
What about the improvement of technology and medicine?
please help me, with this.... three coins are tossed let be the number of head(h)obtain,construct a probability distribution for X
technology and medicine is improving but they are limited
If those conscience of their health, one will live longer periods of life.
hi,why the mean =sum(xi)/n but the variance =sum(xi-xbar)/ n-1 what is the difference between (n or n-1)
Soran Reply
This is hard to type, so I'll use "m" for "x bar", and a few other notations that I hope will be clear: Definition: sqrt(SUM[(x - m)^2] / (n-1)) where m = SUM[x] / n Desired formula: sqrt((SUM[x^2] - SUM[x]^2)/n / (n-1)) Now let's do what you started to do, and see if we can manipulate the definitio
what is the difference between (n ) and (n-1) in the mean and variance
Definition: sqrt(SUM[(x - m)^2] / (n-1)) where m = SUM[x] / n what is the difference between (n and n-1)
Hi, the diference is tha when we estimate parameters in a sample (not in the total population) we need to consider the degrees of liberty for the estimation.
Hie guys, am analysing rainfall data for different stations and i got kurtosis values of 0.7 for one station and 0.4 for another, what can i say about this?
difference in degrees of freedom

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Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
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