Review the information provided below and answer the questions below.

A business researcher is conducting a study to investigate how social media engagement impacts the financial performance of

small and medium$-$sized enterprises $($SMEs$)$ in the Johannesburg Metropolitan Municipality $($JMM$).$ The study also aims to

determine whether the effect of social media engagement differs between SMEs in the manufacturing and service sectors$.$ The

objective is to provide actionable insights for optimising social media strategies to improve financial outcomes for SMEs across

these sectors within the JMM$.$ Understanding these dynamics can assist SMEs in tailoring their social media efforts to enhance

financial performance and gain a competitive advantage.

To measure social media engagement, the researcher used the Social Media Metrics Questionnaire $($SMMQ$)$ framework developed

by Oeldorf$-$Hirsch, Sundar, and Liang $(2023).$ The social media engagement rate $(\%)$ was calculated as the total number of likes,

comments, shares, and clicks divided by the number of followers, expressed as a percentage. Financial performance was

evaluated using firm annual revenue growth $($FRG$)(\%),$ which tracks revenue changes attributable to social media efforts $($Kumar et

al$.,2024).$ An excerpt of the data collected by the researcher is presented in Table $4\mathrm{.}1.$

Table $4\mathrm{.}1$: Excerpt of the data collected by the researcher.

Table $4\mathrm{.}1$: Excerpt of the data collected by the researcher.

Firm Ref # Sector Social Media Spend $($R$)$ Engagement Rate $(\%)$ Firm Annual Revenue

Growth $(\%)$

$1$ M $5000001\mathrm{.}863\mathrm{.}86$

$2$ S $3000001\mathrm{.}545\mathrm{.}26$

$3$ M $6000002\mathrm{.}204\mathrm{.}12$

$4$ S $4000001\mathrm{.}624\mathrm{.}46$

$5$ S $3500001\mathrm{.}445\mathrm{.}88$

$6$ S $3200001\mathrm{.}254\mathrm{.}98$

$7$ M $10000002\mathrm{.}533\mathrm{.}12$

$8$ M $8900002\mathrm{.}452\mathrm{.}14$

$9$ M $9500003\mathrm{.}183\mathrm{.}05$

$10$ S $6600002\mathrm{.}455\mathrm{.}72$

$11$ M $7500002\mathrm{.}132\mathrm{.}65$

$12$ S $7200002\mathrm{.}286\mathrm{.}35$

$13$ S $5600002\mathrm{.}985\mathrm{.}88$

$14$ M $8000003\mathrm{.}563\mathrm{.}75$

$15$ S $6900004\mathrm{.}267\mathrm{.}29$

$16$ M $5900002\mathrm{.}984\mathrm{.}98$

$17$ M $8800003\mathrm{.}464\mathrm{.}04$

$18$ M $11000004\mathrm{.}154\mathrm{.}45$

$...............$

$120$ S $5800002\mathrm{.}114\mathrm{.}12$

Using IBM SPSS Statistics version $26,$ the researcher conducted the data analysis and the output in Figure $4\mathrm{.}1$ to Figure $4\mathrm{.}6$ was

generated.

Figure $4\mathrm{.}1$: Descriptive Statistics

Figure $4\mathrm{.}1$: Descriptive Statistics

Engagement Rate $(\%)$ Firm Annual Revenue Growth $(\%)$

Mean $2\mathrm{.}90$ Mean $4\mathrm{.}98$

Standard Error $0\mathrm{.}0903$ Standard Error $0\mathrm{.}1340$

Median $2\mathrm{.}80$ Median $4\mathrm{.}89$

Mode $2\mathrm{.}22$ Mode $4\mathrm{.}12$

Standard Deviation $0\mathrm{.}9888$ Standard Deviation $1\mathrm{.}4681$

Sample Variance $0\mathrm{.}9776$ Sample Variance $2\mathrm{.}1553$

Kurtosis

$-1\mathrm{.}0521$ Kurtosis $-0\mathrm{.}7577$

Skewness $0\mathrm{.}0515$ Skewness $-0\mathrm{.}0151$

Range $4\mathrm{.}11$ Range $6\mathrm{.}14$

Minimum $1\mathrm{.}11$ Minimum $2\mathrm{.}08$

Maximum $5\mathrm{.}22$ Maximum $8\mathrm{.}22$

Sum $347\mathrm{.}53$ Sum $598\mathrm{.}1$

Count $120$ Count $120$

Figure $4\mathrm{.}2$: Model Summaryb

Model R R Square Adjusted R Square Std$.$ Error of the Estimate

$1\mathrm{.}718$a $\mathrm{.}516\mathrm{.}5121\mathrm{.}0260$

a$.$ Predictors: $($Constant$),$ Social Media Engagement

b$.$ Dependent Variable: Firm Revenue Growth

Figure $4\mathrm{.}3$: ANOVAa

Model Sum of Squares df Mean Square F Sig.

$1$ Regression $132\mathrm{.}2581132\mathrm{.}258125\mathrm{.}633\mathrm{.}000$

b

Residual $124\mathrm{.}2221181\mathrm{.}053$

Total $256\mathrm{.}480119$

a$.$ Dependent Variable: Firm Revenue Growth

b$.$ Predictors: $($Constant$),$ Social Media Engagement

Figure $4\mathrm{.}4$: Coefficientsa

Model

Unstandardized Coefficients

Standardized

Coefficients

B Std$.$ Error Beta t Sig.

$1($Constant$)1\mathrm{.}8963\mathrm{.}29106\mathrm{.}5169\mathrm{.}000$

Social Media Engagement $1\mathrm{.}0662\mathrm{.}0951\mathrm{.}71811\mathrm{.}2086\mathrm{.}000$

a$.$ Dependent Variable: Firm Revenue Growth

Figure $4\mathrm{.}5$: Descriptives

Firm Revenue Growth $(\%)$

N Mean

Std$.$

Deviation

Std$.$

Error

$95\%$ Confidence

Interval for Mean

Minimum Maximum

Lower

Bound

Upper

Bound

Manufacturing SME $553\mathrm{.}74\mathrm{.}707\mathrm{.}09533\mathrm{.}474\mathrm{.}012\mathrm{.}084\mathrm{.}98$

Service SME $656\mathrm{.}04\mathrm{.}752\mathrm{.}09335\mathrm{.}786\mathrm{.}303\mathrm{.}658\mathrm{.}22$

Total $1204\mathrm{.}981\mathrm{.}468\mathrm{.}13404\mathrm{.}605\mathrm{.}362\mathrm{.}088\mathrm{.}22$

Figure $4\mathrm{.}6$: ANOVA

Firm Revenue Growth $(\%)$

Sum of Squares df Mean Square F Sig.

Between Groups $157\mathrm{.}8661157\mathrm{.}866188\mathrm{.}901\mathrm{.}000$

Within Groups $98\mathrm{.}614118\mathrm{.}836$

Total $256\mathrm{.}480119$

REQUIRED:

$4\mathrm{.}1$ Specify THREE $(3)$ research objectives and THREE $(3)$ research questions that the study will attempt to answer. $(6$ marks$)$

$4\mathrm{.}2$ Formulate the null and alternative hypotheses for each of the research questions you have formulated in question

$4\mathrm{.}1.$

$(6$ marks$)$

$4\mathrm{.}3$ Interpret the output presented in Figures $4\mathrm{.}1$ to $4\mathrm{.}6.$ In your interpretation, focus on the observed relationship

between social media engagement and firm revenue growth. In addition, evaluate whether there is a significant

difference in how social media engagement impacts financial performance between SMEs in the manufacturing

sector and those in the service sector.