A family physician wanted to know if age and gender were factors that explained levels of serum cholesterol (in mg/dL) in her adult patients. She randomly selects two patients for each category of data and obtains the following results:

Serum cholesterols are known to be approximately normally distributed and the population variances are equal.
(a) What type of factorial design is this? How many replications are there within each cell?
(b) What is the response variable? What are the two factors?
(c) Determine if there is significant interaction between age and gender.
(d) If there is no significant interaction, determine whether there is significant difference in the means for the three age groups. If there is no significant interaction, determine whether there is significant difference in the means for the genders.
(e) Draw an interaction plot of the data to support the results of parts (c) and (d).
(f) The residuals are normally distributed. Verify this.
(g) If there is significant difference in the means for the three age groups, use Tukey's test to determine which pairwise means differ using a familywise error rate of a = 0.05. If there is significant difference in the means for gender, use Tukey's test to determine which pairwise means differ using a familywise error rate of a = 0.05.

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Gender Age (years) 18–34 55 and older 35-54 205, 226 213, 222 218, 231 203, 185 Female 180, 192 175, 193 Male