Staff at Glasgow Dental Hospital carried out a study to examine the dental health of $5-$year$-$old children living in Glasgow. Each of $360$ children had a dental examination under standard conditions and the number of decayed, missing and filled teeth was recorded.Also recorded were the sex of the child, whether they were currently registered at a dentist and the deprivation category of the area $($postcode sector, such as G$128,$ or KA$257)$ the child lived in$.$ The researchers$$ question of interest was whether $5-$year$-$old children living in deprived areas have worse oral health than $5-$year$-$old children living in more affluent areas.Variables in data file:

RefNumber Child reference number $($for admin purposes$)$

DepCat Deprivation category $($on a $1-7$ scale, where $1$ is most affluent

and $7$ is most deprived$).$ In the catchment area for this study,

all the postcode sectors were in DepCat $4,6$ or $7$

RegCat String $($character$)$ variable, with $3$ categories:

NotReg $$ never registered with a dentist;

Lapsed $$ previously registered but now lapsed;

Reg $$ currently registered with a dentist

Sex $1=$ boys, $2=$ girls

DFMT Number of teeth with active decay, that are filled or are missing

a$)$ Using either Minitab or SPSS$,$ obtain appropriate descriptive statistics and

suitable plots for the variables Sex, DepCat, RegCat and DFMT individually $($i$.$e$.$

do not look at any relationships between these variables$).$ Provide a short

interpretation of the output you produce for each variable. Here's data below RefNumber DepCat RegCat Sex DFMT

$27$ NotReg $24$

$87$ NotReg $11$

$97$ NotReg $20$

$137$ Reg $14$

$197$ NotReg $21$

$207$ Reg $215$

$237$ Lapsed $116$

$257$ Reg $26$

$317$ Reg $13$

$497$ NotReg $10$

$547$ Reg $26$

$557$ NotReg $13$

$647$ NotReg $23$

$657$ NotReg $210$

$737$ NotReg $22$

$757$ Reg $18$

$857$ NotReg $22$

$877$ NotReg $22$

$887$ NotReg $22$

$907$ NotReg $111$

$917$ Reg $116$

$927$ Lapsed $27$

$957$ NotReg $14$

$967$ Reg $20$

$977$ NotReg $25$

$987$ NotReg $12$

$1017$ Reg $112$

$1047$ Reg $14$

$1057$ Reg $26$

$1077$ Reg $29$

$1107$ Reg $29$

$1127$ NotReg $13$

$1137$ NotReg $19$

$1187$ Reg $28$

$1217$ NotReg $210$

$1287$ Reg $24$

$1557$ Reg $14$

$2067$ Lapsed $10$

$2086$ NotReg $28$

$2116$ NotReg $22$

$2146$ Reg $27$

$2196$ Reg $27$

$2236$ Reg $20$

$2276$ Reg $20$

$2416$ Reg $212$

$2426$ Reg $12$

$2436$ NotReg $22$

$2494$ NotReg $213$

$2514$ Reg $18$

$2526$ Reg $16$

$2546$ NotReg $20$

$2586$ NotReg $17$

$2594$ NotReg $12$

$2606$ Reg $111$

$2626$ NotReg $21$

$2636$ Reg $23$

$2646$ NotReg $20$

$2696$ NotReg $20$

$2716$ Reg $28$

$2736$ Reg $20$

$2746$ NotReg $10$

$2794$ Reg $10$

$2826$ NotReg $28$

$2846$ Reg $25$

$2914$ Reg $26$

$2924$ NotReg $20$

$2964$ Reg $17$

$3014$ Reg $12$

$3024$ Reg $215$

$3124$ Reg $20$

$3224$ NotReg $10$

$3237$ Reg $20$

$3284$ NotReg $21$

$3306$ Lapsed $111$

$3324$ Reg $10$

$3336$ Reg $12$

$3384$ Reg $10$

$3394$ Reg $10$

$3406$ Reg $10$

$3414$ Reg $18$

$3446$ Reg $20$

$3454$ Reg $12$

$3516$ Reg $17$

$3534$ Reg $22$

$3624$ Reg $16$

$369$ NotReg $13$

$3777$ Reg $23$

$3817$ Reg $20$

$3876$ Lapsed $212$

$3916$ Lapsed $10$

$3976$ Reg $23$

$4036$ Reg $111$

$4136$ Reg $22$

$4146$ Reg $20$

$4156$ NotReg $28$

$4217$ NotReg $15$

$4304$ NotReg $211$

$5427$ Lapsed $12$

$5447$ Reg $10$

$5487$ NotReg $15$ b$)$ Using either Minitab or SPSS carry out a $2-$sample t$-$test and confidence

interval to investigate whether there is a difference between oral health, as

measured by DFMT$,$ in the poorest areas $($DepCat $7)$ and in less deprived areas.