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Statistics 106: Practice Final

1. (15 points). Answer the following questions.

(a) Suppose you are an investigator and you want to study the eﬀects of three blood pressure lowering

drugs. Suppose you also know that, gender is like to have an eﬀect. Describe how you should conduct the study. Your description should explain how to assign patients to treatment groups, as well as strategies to account for potential confounding factors.

(b) Can we apply Tukey’s procedure for pairwise comparisons that were not pre-speciﬁed, but rather

chosen after looking at the data? Explain.

2. (20 points). The following interaction plots are based on the treatment means of two-factor ANOVA models. For each case, please answer the following:

i. Does Factor A have any eﬀects? Does Factor B have any eﬀects? Explain.

ii. Does Factor A have any main eﬀects? Does Factor B have any main eﬀects? Explain.

iii. Are there interaction eﬀects between these two factors? Explain.

3. (35 points) A scientist was interested in ﬁnding out the location of genes which control cholesterol level in mouse. She thought she had located a major gene which has three coding types (A,B and O). The cholesterol levels of 89 mice and their gene types were recorded and the summary statistics are given below.

(a) Given the mean squared error being 0.1018, derive the ANOVA table. You need to show your

work for full credit.

(b) Test whether or not the mean cholesterol level is the same for these three gene types at the

signiﬁcance level 0.05. State the null and alternative hypotheses, the decision rule, and the conclusion.

(d) Obtain a 95% conﬁdence interval for the error standard deviation.

(e) After examining the data, the scientist suspected that there is likely a diﬀerence between the

mean cholesterol level of gene type B and that of gene type A or O. How should the scientist test whether or not her conjecture is supported by data? Conduct the test at 0 .05 level.

4. (30 points). A cloud service company employed a large number of frontend customer service agents and backend technical support agents. The company wanted to investigate the eﬀects of these agents on customer satisfaction. Five customer service agents and four technical support agents were randomly selected. Four customers were randomly assigned to each customer service agent and technical support agent combination. Customer satisfactory ratings (the higher the rating, the more satisﬁed) from an after service survey were recorded. The ANOVA table is given below:

(a) Explain which model should be used to analyze this data. Write down the model equation, model

assumptions and constraints (if any).

(b) Test whether or not there are customer service and technical support interaction eﬀects at the

signiﬁcance level 0.05. State the null and alternative hypotheses, decision rule and the conclusion.

(c) Test whether or not there are technical support agent main eﬀects at the signiﬁcance level 0 .05. State the null and alternative hypotheses, decision rule and the conclusion.

(d) If only one customer had been assigned to each customer service agent and technical support agent combination, would it still be possible to test the presence of the technical support agent main eﬀects? Explain.