DATA ANALYTICS & BUSINESS INTELLIGENCE

QUESTION 1
The AIS collects a variety of data on its athletes. In one publically-av ailable data set, measurements were made on 202
athletes of various body and blood characteristics. The sum of skin folds (ssf), a measure of body fat, was recorded. Interest is at the
momentturning to extracting intelligence about the relationship between ssf and pbfat.
(a) What is the correlation between ssf and
pbfat?
(b) Explain what your value of the correlation means in one or two sentences.
(c) Write down the equation of the regression
line relating ssf (a fairly simple measure to take) to pbfat (a much more complex measure to take).
(d) Explain what your value of the
intercept means in one or two sentences.
(e) Explain what your value of the slope means in one or two sentences.
QUESTION 2 10
marks
(a) What is the predicted percentage of pbfat for a ssf of 70?
(b) Carry out a hypothesis test to check whether there is
evidence in the sample of a non-zero slope for the line relating ssf to pbfat. Your answer should include null and alternative hypotheses,
test statistic, p-value and conclusion.
(c) Write down a 95% confidence interval for the slope for the line relating ssf to pbf at in all
athletes.
(d) Explain what the confidence interval in (e) means in one or two sentences.
(e) Produce a scatter plot of residuals
versus predicted values. Use the plot to comment on whether the regression inference conditions of constant variance and no strong outliers
have been met by this data set.
QUESTION 3 10 marks
Coaches would now like to extract intelligence about whetherthere is evidence
of a difference in average haematocrit levels (a blood marker, denoted hc) between male and female athletes, on the basis of the data
collected.
(a) Write down the null and alternative hypotheses for the researchers.
(b) Why should this be an independent-samples test
and not a paired-samples test? Answer o one or two sentences.
(c) Use P to find the value of the test statistic, and the p-value, for
this test.
(d) At the 5% level, is the null hypothesis rejected or not? Explain your answer in one or two sentences.
(e) Write a
conclusion to the test for the researchers.
QUESTION4 lOmarks
The relationship between sport and gender is also of interest.
Use
P to carry out a chi-squared test for the researchers. Your answer should include null and alternative hypothesis, a test statistic, p
value, decision and conclusion that can be reported to the researchers
QUESTION 5
Sports managers are interested in whether ssf
depends on the sport the athletes play.
(a) Produce a well-labelled boxplot of ssf by sport.
(b) Calculate the mean and the standard
deviation of the tennis players’ ssf. Compare the location and spread of the ten sports in a short paragraph.
(c) Check whetherthe
condition of equal standard deviations between the ten groups has been met. Your answer should include some calculations.
(d) Use an
ANOVAto test the hypothesis of no difference in mean ssf between the five sports. Your answer should include a null and alternative
hypothesis, test statistic, p value and conclusion. Use a = 0.05.
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