Question $4$

$(20$ Marks$)$

Utilising the statistical decision$-$making tree, in each of the following studies $(4\mathrm{.}1$ to $4\mathrm{.}5)$:

identify the independent and dependent variables

$,$ specify the appropriate statistical test you would run

briefly explain why you selected the test, and

state the parametric and non$-$parametric equivalents of the test

$4\mathrm{.}1.$ Twitter's recent rebranding to $"$X$"$ reflects a strategic shift under the ownership of Elon Musk. This shift is in line with the vision for transforming Twitter into a "super app" as well as an attempt to distinguish itself from competitors and it signals significant changes in its offerings and capabilities. The rebranding reflects an adaptation to evolving technological trends and cultural shifts. A team of researchers wants to determine if this change has had an impact on sales.

$(4$ marks$)$

$4\mathrm{.}2.$ Company XYZ Limited, recently completed a training and development programme for employees. The training and development manager wants to evaluate the impact of the training and development on employee performance.

$(4$ marks$)$

$4\mathrm{.}3.$ Mrs$.$ Cynthia Mbale, the operations manager of MTH Ltd$,$ a manufacturing company that produces a popular consumer product, has noted recent increases in absenteeism over the past $10$ months. She plans to investigate the impact absenteeism has had on organisational performance. Mrs$.$ Mbale accessed productivity data on how many units of the product are produced weekly, over a period of two years. $(4$ marks$)$

$4\mathrm{.}4.$ A salesperson for a major car brand aims to examine the association between an individual's type of employment and their preference for purchasing either a new or used car.

$(4$ marks$)$

$4\mathrm{.}5.$ A medical researcher aims to compare the relative impact of classical music versus contemporary music on the cognitive development of grade R children $($aged five years$).$ Two groups of $20$ grade R children each were randomly selected from primary school for the study. Group A listened to classical music for $30$ minutes at the start of each day from Monday to Friday, while Group B listened to contemporary music during the same period in a separate classroom. Cognitive development was measured for both groups at the beginning of the study and after one month.

Given that the scores for Group B are heavily skewed, which statistical test should be used to assess the hypothesis that the two music genres have differential impacts on cognitive development?

$(4$ marks$)$