STATISTICS
3N03
TEST #3 -
2000-11-23
Instructions
Aids permitted: any
calculators, any tables and one sheet of notes (8.5" x 11", one side
only). If the tables are in a textbook, elastic bands must be drawn
around the remaining pages so that only the tables can be
used.
Questions
- Define the following terms:
parameter, pivotal
quantity, hypothesis, simple hypothesis, P-value. [5
marks]
- The loads at specimen failure (in
MPa) for 6 U-700 alloy specimens were 19.8, 18.5, 17.6, 16.7,
15.8, 15.4.
(a) Assuming s = 4, do a two-sided 5% test of the
hypothesis that the mean load at failure is 15 MPa. State any
other assumptions you make. [5 marks]
(b) Compute a two-sided 95% confidence interval for the population
standard deviation and use it to test the hypothesis that
s =
4. State any assumptions you make. [5 marks]
(c) Repeat (a), without assuming that s = 4.
[5 marks]
- The standard deviation of a
titration assay is known to be 0.012 units. If you wish to test a
hypothesis about the mean at the 1% level of significance, and
have a 90% chance of identifying cases where the true mean is 0.01
units from the hypothesized value in either direction, what sample
size will you need? [5
marks]
- A coin was tossed 6 times and
came up heads each time. Compute a P-value to test the hypothesis
that the coin is unbiased. State any assumptions you make.
[5 marks]