91Ó°ÊÓ

The given data is

The level of significance $\mathrm{Î\pm }=0.10$

Let us see the below test hypothesis

Null hypothesis

$H_0$: There is no difference exist in mean body length among minke whales entangled at the four different depths

Alternative hypothesis

$H_a$: There is a difference exist in mean body length among minke whales entangled at the four different depths

The mean of all observations is

$\stackrel{¯}{x}=\frac{39(4.49)+20(5.06)+28(5.75)+14(5.99)}{39+20+28+14}$

$=5.160$

The treatment sum of squares is

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

$=39(4.49-5.160{)}^2+20(5.06-5.160{)}^2+28(5.75-5.160{)}^2$

$+14(5.99-5.160{)}^2$

$=37.099$

The error sum of squares is

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

$=(39-1)(0.80{)}^2+(20-1\left)\right(0.79{)}^2+(28-1)(1.20{)}^2$

$+(14-1)(0.97{)}^2$

$=87.290$

The total sum of squares is

$SST=SSTR+SSE$

$=37.099+87.290$

$=124.389$

The mean treatment of sum of squares is

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

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

$=12.36$

The mean error of the sum of squares is

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

$=\frac{89.290}{101-4}$

$=0.900$

The $F-$static is

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

$=\frac{12.366}{0.900}$

$=13.74$

From the given data

$F-$static $(13.74)>$critical value $(3.99)$

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 results show that there is a variation in mean body length across minke whales entangled at four different depths.