$\backslash$table$[[54,62,63,45],[57,57,45,63],[61,59,70,56],[54,63,73,57],[61,62,55,55],[36,55,54,53],[53,48,45,52],[62,62,63,71],[43,57,53,62],[44,58,37,58],[49,62,44,46],[52,43,41,56],[33,59,54,72],[55,45,53,46],[60,61,41,66],[48,52,39,54],[46,59,51,59],[57,60,50,58],[59,45,56,51],[62,56,61,45],[$dots$,$dots,dots,dots$],[62,60,59,64],[$n$=30,$n$=30,$n$=30,$n$=30]]$

Using IBM SPSS Statistics version $27,$ Dr Sithole undertook the data analysis and generated the output shown below in

Figure $3\mathrm{.}1$ to Figure $3\mathrm{.}6.$ Figure $3\mathrm{.}1$:

Case Processing Summary

Figure $3\mathrm{.}2$:

Descriptives

Employee$\_$Productivity

Figure $3\mathrm{.}3$:

DescriptivesFigure $3\mathrm{.}4$:

Figure $3\mathrm{.}5$:

Tests of Normality

$*.$ This is a lower bound of the true significance.

a$.$ Lilliefors Significance CorrectionFigure $3\mathrm{.}8$:

Multiple Comparisons

Dependent Variable: Employee$\_$Productivity

Tukey HSD

${?}^{***}.$ The mean difference is significant at the $0\mathrm{.}05$ level. Figure $3\mathrm{.}9$:

Employee$\_$Productivity

Means for groups in homogeneous subsets are displayed.

a$.$ Uses Harmonic Mean Sample Size $=24\mathrm{.}490.$

b$.$ The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error levels are not guaranteed.

Figure $3\mathrm{.}10$:

Profile plotsREQUIRED:

$3\mathrm{.}1$ 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 $3\mathrm{.}2.$ QUESTION $3$

$(20$ Marks$)$

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$).$

Table $3\mathrm{.}1$: The productivity scores of $120$ employees employed across Gauteng$-$based family$-$owned construction firms with different ownership structures.

$\backslash$table$[[$Sole proprietorship,Partnership,Co$-$operative,Public Company$],[54,55,54,64],[47,45,53,58],[54,47,45,73],[62,39,47,57],[36,60,57,56]]$