1.1

  1. Categorical, nominal

  2. Numerical, continuous

  3. Categorical, nominal

  4. Numerical, discrete

  5. Categorical, ordinal

  6. Numerical, continuous

1.2

By the empirical rule (the sample is fairly large) we consider the interval \(\bar{x} \pm 2 S\) to be a fair approximation of an interval containing 95% of durations. Clearly this could be valuable for planning. E.g. \(56 + 2\cdot 11 = 78\) minutes would be an upper limit for almost all operations.

1.3

  1. Considering the points with around 50 years of life expectancy, a point guess of about 20 seems reasonable. An interval from 0 - 50% appears likely to contain the number.

  2. At 80 years, we might guess 70% urbanization. An interval guess could be 40 - 95%.

  3. No. Clearly, a developed and industrialized country will normally have more urbanization as well as a more developed health care system. Thus, some hidden variables may well cause the correlation. This means that the level of development in a country affects both of the observed variables, which then become correlated. However, there is no reason to believe in a direct causal effect from high urbanization to high expected lifelength. The causation lies in the level of development, which is hidden when we only consider the two variables in the question isolated. This “phenomenon” is very common in statistics and quite often leads to false interpretation of correlation as causation. We should always think about the possibility for hidden variables when someone shows a correlation result. The effect can be illustrated with the figure below, where blue arrows are causal relations, and the red arrow is suspected to be a correlation relationship with little or no causal explanation.

Visualizing hidden variables effect