91Ó°ÊÓ

The given data is

The level of significance $\mathrm{Î\pm }=0.01$

Let us see the test hypothesis

Null hypothesis

$H_0$: There is no difference exist in Mean starting salaries among bachelor's degree candidates in the six fields.

Alternative hypothesis

$H_a$: There is no difference exist in Mean starting salaries among bachelor's degree candidates in the six fields.

The mean of all observations is

$\stackrel{¯}{x}=\frac{46(55.1)+11(44.6)+30(59.1)+11(40.6)+44(62.6)+18\left(43\right)}{46+11+30+11+44+18}$

$=54.83$

The treatment sum of squares is

$SSTR=∑n_i{\left({\stackrel{¯}{x}}_i-\stackrel{¯}{x}\right)}^2$

$=46(55.1-54.833{)}^2+11(44.6-54.833{)}^2+30(59.1-54.833{)}^2$

$+11(40.6-54.833{)}^2+44(62.6-54.833{)}^2$$+18(43-54.833{)}^2$

$=9104.43$

The error sum of squares is

$SSE=∑\left(n_i-1\right){\left(s_i\right)}^2$

$=(46-1)(5.6{)}^2+(11-1\left)\right(4.7{)}^2+(30-1)(4{)}^2$

$+(11-1)(5{)}^2+(44-1\left)\right(5.7{)}^2+(18-1)(4.8{)}^2$

$=4134.85$

The total sum of squares is

$SST=SSTR+SSE$

$=9104.4310+4134.85$

$=13239.2810$

The mean treatment sum of squares is

$MSTR=\frac{SSTR}{k-1}$

$=\frac{37.099}{4-1}$

$=12.36$

The mean error sum of squares is

$MSE=\frac{SSE}{n-k}$

$=\frac{4134.85}{160-6}$

$=26.85$

The $F-$static is

$F-static=\frac{MSTR}{MSE}$

$=\frac{1820.886}{26.85}$

role="math" localid="1652207470757" $=67.817$

$F-$static $(67.817)>$critical value $(3.14)$

As a result, the crucial value approach

At a $1\%$significant threshold, the null hypothesis is rejected.

As a result, the results are statistically significant at the $1\%$level.

As a result, the statistics show that there is a disparity in mean starting earnings among bachelor's degree candidates in the six fields.