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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' (Trans. Amer. Fisheries Soc. (1991: 405-420) gave the accompanying data on 10 values for the data sets where 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) −90.020 16.710 −5.387 0.000
Length 0.705 0.048 14.566 0.000

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

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temmydbrain

Answer:

Check the explanation

Step-by-step explanation:

sample size n=                                          10  

number of independent variables p=        1  

degree of freedom =n-p-1=                        8  

estimated slope b=                                   0.71  

standard error of slope=sb=                  0.0480

for 95 % confidence and 8 degree

of freedom critical t=                                  2.31

95% confidence interval =

b1 -/+ t*standard error=                          (0.6,0.82)

Ver imagen temmydbrain
MrRoyal

The 95% confidence interval for the slope is (0.594, 0.816)

From the table, we have the following parameters

[tex]\mathbf{b =0.705}[/tex] --- the slope

[tex]\mathbf{sb =0.048}[/tex] --- the standard error of the slope

[tex]\mathbf{n =10}[/tex] -- the sample size

The degree of freedom is calculated using

[tex]\mathbf{df = n -2}[/tex]

So, we have:

[tex]\mathbf{df = 10 -2}[/tex]

[tex]\mathbf{df = 8}[/tex]

At 95% confidence interval, and degrees of freedom of 8;

The critical value is:

[tex]\mathbf{t_{\alpha/2} = 2.31}[/tex]

The confidence interval is then calculated as:

[tex]\mathbf{CI =(b \pm Sb \times t_{\alpha/2} )}[/tex]

This gives

[tex]\mathbf{CI =(0.705 \pm 0.048\times 2.31)}[/tex]

[tex]\mathbf{CI =(0.705 \pm 0.111)}[/tex]

Split

[tex]\mathbf{CI =(0.705 -0.111, 0.705 +0.111)}[/tex]

[tex]\mathbf{CI =(0.594, 0.816)}[/tex]

Hence, the 95% confidence interval is (0.594, 0.816)

Read more about confidence intervals at:

https://brainly.com/question/2193959

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