Let X1, X2, X3, X4 equal the cholesterol level of a woman under the age of 50, a man under 50, a woman 50 or older, and a man 50 or older, respectively. Assume that the distribution of Xi is N(μi, σ2), i = 1, 2, 3, 4. We shall test the null hypothesis H0: μ1 = μ2 = μ3 = μ4, using seven observations of each Xi.
(a) Give a critical region for an α = 0.05 significance level.
(b) Construct an ANOVA table and state your conclusion, using the following data:

(c) Give bounds on the p-value for this test.
(d) For each set of data, construct box-and-whisker diagrams on the same figure and give an interpretation of your diagram.

x 221 213 202 183185 197 162 x2: 27 192 189 209 227 236 142 r: 262 193 224 201 1 178 265 x4 12253 248 278 232 267 289