Page 187 - Applied Statistics Using SPSS, STATISTICA, MATLAB and R

Exercises 167

4.5 Consider the Programming dataset containing student scores during the period 1986-
88. Test at 5% level of significance whether or not the mean score is 10. Study the
power of the test.

4.6 Determine, at 5% level of significance, whether the standard deviations of variables CG
and EG of the M oulds dataset are larger than 0.005 mm.

4.7 Check whether the correlations studied in Exercises 2.9, 2.10. 2.17, 2.18 and 2.19 are
significant at 5% level.

4.8 Study the correlation of HFS with I0A = |I0 − 1235| + 0.1, where HFS and I0 are
variables of the Breast Tissue dataset. Is this correlation more significant than the one
between HFS and I0S in Example 2.18?

4.9 The CFU datasheet of the Cell s dataset contains bacterial counts in three organs of
sacrificed mice at three different times. Counts are performed in the same conditions in
two groups of mice: a protein-deficient group (KO) and a normal, control group (C).
Assess at 5% level whether the spleen bacterial count in the two groups are different
after two weeks of infection. Which type of test must be used?

4.10 Assume one wishes to compare the measurement sets CG and EG of the Mo ulds
dataset.
a) Which type of test must be used?
b) Perform the two-sample mean test at 5% level and study the respective power.
c) Assess the equality of variance of the sets.

4.11 Consider the CT G dataset. Apply a two-sample mean test comparing the measurements
of the foetal heart rate baseline (LB variable) performed in 1996 against those
performed in other years. Discuss the results and pertinence of the test.

4.12 Assume we want to discriminate carcinoma from other tissue types, using one of the
characteristics of the Breast T issue dataset.
a) Assess, at 5% significance level, whether such discrimination can be achieved
with one of the characteristics I0, AREA and PERIM.
b) Assess the equality of variance issue.
c) Assess whether the rejection of the alternative hypothesis corresponding to the
sample means is made with a power over 80%.

4.13 Consider the Infarct dataset containing the measurements EF, IAD and GRD and a
score variable (SCR), categorising the severeness of left ventricle necrosis. Determine
which of those three variables discriminates at 5% level of significance the score group
2 from the group with scores 0 and 1. Discuss the methods used checking the equality
of variance assumption.

4.14 Consider the comparison between the mean neonatal mortality rate at home (MH) and
in Health Centres (MI) based on the samples of the Neonatal dataset. What kind of
test should be applied in order to assess this two-sample mean comparison and which
conclusion is drawn from the test at 5% significance level?