Question

ANOVA hypotheses—A researcher interested in investigating the effectiveness of two drugs randomly divides 150 volunteers into five equal groups—placebo, double dose of drug 1, single dose of drug 1, double dose of drug 2, single dose of drug 2—then measures the platelet level of each patient.

Write the appropriate hypotheses to test the hypotheses that at least one of the population mean platelet levels for these treatments are different. Be sure to identify your parameter and label your groups appropriately.

Answer 1

Let Group 1: Placebo

Group 2: Double dose of drug 1

Group 3: Single dose of drug 1

Group 4: Double dose of drug 2

Group 5: Single dose of drug 2

There are 30 patients in each group. We measure the platelet level of each group. We want to test if the population mean platelet of any of the groups is significantly different from the others. So, we are testing,

H0: u1=u2=u3=u4=u5 vs

H1: u1 not equal u2 not equal u3 not equal u4 not equal u5

To test this hypothesis, we are performing a one way ANOVA, with numerator df: k-1= 4, and denominator df: N-k= 145