Study the information provided below and answer the following questions.

Family business $($FB$)$ is a very important phenomenon around the world and deserves the attention of researchers for a

number of reasons. Traditionally, the definition of family businesses $($FBs$)$ involves one or more members of a family

wielding considerable control over the company, due to their significant percentage of ownership $($Leotta and Ruggeri,

$2020).$

Globally, FBs constitute the predominant form of ownership in most markets and findings gleaned from publicly listed firms

may not apply to the ubiquitous, but less frequently studied, privately held family firm $($Rothwell and Prescott, $2022).$ There

is a theoretical notion that family involvement has an effect on the factors of production from a productivity standpoint. In a

recent study, Alves and Gama $(2020)$ reported that family labour output contributions are significantly higher, and family

capital output contributions lower.

Dr Ken Sithole, a business researcher with an interest in the productivity of family businesses is investigating the impact of

family business ownership structure on employee productivity in the construction sector in the Gauteng Province. The

overarching objective of Dr Sithole$$s study is to determine whether there are significant differences in employee productivity

across the four types of family business ownership in the construction sector in the Gauteng Province.

Using a validated and reliable instrument, Dr Sithole measured the productivity of $120$ employees working at a number of

family$-$owned construction firms. The ownership structures of construction firms involved in the study ranged from sole

proprietorships, partnerships, cooperatives, and public company $($corporations$).$ Of the $120$ employees surveyed, $30$ were

employed at sole proprietorships, partnerships, cooperatives, and corporations respectively $($see Table $3\mathrm{.}1,$ below$).$

REQUIRED:

$3\mathrm{.}1$ Specify the aim and the research design of Dr Sithole$$s study. $(4$ marks$)$

$3\mathrm{.}2$ Formulate the null and alternative hypotheses for Dr Sithole$$s study. $(2$ marks$)$

$3\mathrm{.}3$ Identify and elaborate on the independent and dependent variables of Dr Sithole$$s study. $(2$ marks$)$

$3\mathrm{.}4$ Comment on the output in Figure $3\mathrm{.}3$ to Figure $3\mathrm{.}6$ and highlight the implications for the

subsequent analyses performed in Dr Sithole$$s study.

$(6$ marks$)$

$3\mathrm{.}5$ On the basis of the output in Figure $3\mathrm{.}7$ to Figure $3\mathrm{.}10,$ provide a comprehensive interpretation of

the outcome of the hypothesis test formulated in $3\mathrm{.}2.$

$(6$ marks$)$