(a) What does the Student t variable express? Write down an expression for the
Student t variable for a small sample (N) of measurements in terms of the mean
of the sample (xmean), the standard deviation (sx) of the sample, and the mean
(m) of the whole population of which the sample is part:
(b) Sketch typical t distribution curves for sample sizes of 2, 11, and infinity.
(c) Sketch a t distribution curve that shows the meaning of the term a, which is
commonly used to express the level of confidence that t is less than some value
ta.
(d) Use a t distribution table to calculate the value of t for a sample of 21 measurements and a confidence level of 99%.
The measurements are divided into 9 data bins with boundaries at 859.5, 876.5,
893.5, 910.5, 927.5, 944.5, 961.5, 978.5, 995.5, 1012.5.
The measurement count in bin 1 from 869.5 to 886.5 days is 3 and the count in the
other successive bins is 11, 27, 39, 46, 40, 24, 8 and 2.