Question

Suppose we to test H₀: η = 4.5 vs. H_a: η< 4.5, where η is the population median. Among n= 10 observations, let S be the number of the measurements which are larger than 4.5. Under H₀, S follows a binomial(n= 10,p = 0.5).

1) Which of the following sample results gives the strongest evidence to support H_a?

a. S=4

b. S=5

c. S=6

d. They are all the same

2) Following the problem, suppose S = 1, what is the p-value?

a. 0.0010

b. 0.0107

c. 0.9893

d. 0.9990

Answer 1

1)

To support Ha  η< 4.5. So, S (the number of the measurements which are larger than 4.5) will be less.

Thus, the lowest value of S will gives the strongest evidence to support Ha

a. S=4

2)

For S = 1, only one of the measurements out of 10 is greater than 4.5

P-value = P(S 1 | S ~ binomial(n= 10,p = 0.5))

= P(S = 0) + P(S = 1)

b. 0.0107