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

 

  1. Define the following terms: parameter, pivotal quantity, hypothesis, simple hypothesis, P-value. [5 marks]

  2. 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]

  3. 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]

  4. 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]

Statistics 3N03