1.1 Visualising the data and checking assumptions

As usual, it is a good idea to visualise the data as this can give us a good overview and help us understand what we are analysing. The below plot is called a "stacked bar chart" (or "stacked bar plot") and provides a visual breakdown between regular Facebook users (76%) and irregular Facebook users (24%).

To carry out the hypothesis test, we can use the Normal distribution since the estimated proportion is approximately normally distributed, due to the Central Limit Theorem. (Note: some statistical software packages apply a small 'continuity correction' to the estimates that provides slightly improved confidence intervals.) However, this means that the following condition applies:

One-sample test of proportion condition:

\(np \geq 5\) and \(n(1 - p) \geq 5\).

If the above condition is met, we have that

\[\hat{P}\stackrel{\tiny \text{approx.}}\sim N\left(p,\frac{p(1 - p)}{n}\right). \]

Let's now check and see whether the condition has been met (note that for \(p\), we will use \(p_0 = 0.73\)):

  • \(np = 474\times 0.73 = 346.02\) which is greater than 5
  • \(n(1 - p) = 474\times (1 - 0.73) = 474\times (0.27) = 127.98\) which is greater than 5.

Therefore, the condition has been met and we are now ready to carry out the hypothesis test.