91影视

The data represents the trap spacing measurements (in meters) for a sample of seven teams of red spiny lobster fishermen.

The 90% confidence interval can be calculated using the formula.

$\frac{\left(n-1\right)s^2}{{蠂}_{\frac{伪}{2}}^2}猢�{蟽}^2猢�\frac{\left(n-1\right)s^2}{{蠂}_{1-\frac{伪}{2}}^2}$

From the given data,

The sample mean is calculated using the following formula,

$\stackrel{炉}{x}=\frac{1}{n}\underset{i=1}{\overset{n}{鈭�}}{x}_i$

Therefore,

$\begin{array}{rcl}\stackrel{炉}{x}& =& \left(\frac{93+99+...+86}{7}\right)\\ & =& \frac{629}{7}\\ & =& 89.85\\ & & \end{array}$

Also, sample variance is calculated using the following formula,

${蟽}^2=\frac{1}{n-1}\underset{i=1}{\overset{n}{鈭�}}{\left(x_i-\stackrel{炉}{x}\right)}^2$

$$\begin{gathered} =\frac{1}{6}\left({\left(93-89.85\right)}^2+...+{\left(86-89.85\right)}^2\right) \\ =\frac{1}{6}\left({\left(3.15\right)}^2+...+{\left(-3.85\right)}^2\right) \\ =\frac{1}{6}\left(9.9225+...+14.8225\right) \end{gathered}$$

$=135.2569$

Therefore, the standard deviation is

$\begin{array}{rcl}蟽& =& \sqrt{135.2569}\\ & =& 11.63\\ & & \end{array}$

From the table values, at the 0.01 level of significance and 6 degrees of freedom, the value for ${蠂}_{\frac{伪}{2}}^2$is 18.5476, and the value for${蠂}_{\left(1-\frac{伪}{2}\right)}^2$ is 0.6757.

Substitute the values to get the required confidence interval.

$$\begin{gathered} \frac{\left(7-1\right){11.63}^2}{18.54758}猢�{蟽}^2猢�\frac{\left(7-1\right){11.63}^2}{0.67572} \\ 43.7545猢�{蟽}^2猢�1200.99 \end{gathered}$$

Therefore, the 99% confidence interval ${蟽}^2$is (43.7546, 1200.99).

From the 99% confidence interval, it can conclude that it is 99% confident that the true variance of trap spacing measurements or red spiny lobster fishermen lies between 43.77546 meters and 1200.99 meters.