Question

Q6. (Exercise 1.55) Mercury poisoning of wading birds. According to a University of Florida wildlife ecology and conservation researcher, the average level of mercury uptake in wading birds in the Everglades is declining (UF News, December 15, 2000). Last year, the average level was 15 parts per million. (a) Give the nu and alternative hypotheses for testing whether the average level this year is less than 15 ppm. (0.5 pt) (b) Describe a Type I error for this test. (Not merely repeat the general definition of Type I error) (0.5 pt) (c) Describe a Type II error for this test. (0.5 pt)

Answer 1

6)

a)

The null and alternate hypothesis are:
H0: $\mu=15$

Ha: $\mu<15$

b)

Now,

P[Type 1 error] = P(Reject H0 | H0 is true) = P(Reject H0 | $\mu=15$ )

c)

Also,

P[Type 2 error] = P(Accept H0 | Ha is true) = P(Accept H0 | $\mu<15$ )