The decline of salmon fisheries along the Columbia River in Oregon has caused great concern among commercial and recreational fishermen. The paper 'Feeding of Predaceous Fishes on Out-Migrating Juvenile Salmonids in John Day Reservoir, Columbia River' gave the accompanying data on y = maximum size of salmonids consumed by a northern squaw fish (the most abundant salmonid predator) and x = squawfish length, both in mm. Here is the computer software printout of the summary:

Coefficients:
Estimate Std. Error t value Pr(> |t|)
(Intercept) -89.010 16.702 -5.329 0.000
Length 0.740 0.047 15.678 0.000

Using this information, compute a 95% confidence interval for the slope.

The estimation for the slope on this case is

And the associated standard error is

For the critical value we need to find the degrees of freedom given by:

Since we don't have the sample size we can assume it large enough to consider the normal approximation to the t distribution and on this case the critical value for 95% of confidence would be

The confidence interval would be between (0.648, 0.832)

Step-by-step explanation:

We are assuming that the estimation was using the least squares method

For this case we need to calculate the slope with the following formula:

Where:

Nowe we can find the means for x and y like this:

And we can find the intercept using this:

The confidence interval for this case is given by this formula:

The estimation for the slope on this case is

And the associated standard error is

For the critical value we need to find the degrees of freedom given by:

Since we don't have the sample size we can assume it large enough to consider the normal approximation to the t distribution and on this case the critical value for 95% of confidence would be

And replacing we got:

The confidence interval would be between (0.648, 0.832)

; )

step-by-step explanation: ; )