For each of the following tests, find:

• E(T) and Var(T)

• The test statistic when approximating to the normal distribution. Also state whether you would reject or not reject the null hypothesis.

a. H₀: the population median is 142.1.

H₁: The population median is less than 142.1.

5% significance level

T = 175, n = 30

b. H₀: the population median is 40.6.

H₁: the population median is not 40.6.

10% significance level

T = 59, n = 20

c. H₀: the population median is 16.3.

H₁: the population median is greater than 16.3.

2.5% significance level

T = 260, n = 40