Question

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.

Answer 1

To compute a 95% confidence interval for the slope, use the formula: Lower bound = Estimate - (critical value x standard error) and Upper bound = Estimate + (critical value x standard error). Using the given values, the 95% confidence interval for the slope is (0.588, 0.822).

Step-by-step explanation:

To compute a 95% confidence interval for the slope, we can use the formula:

Lower bound: Estimate - (critical value x standard error)

Upper bound: Estimate + (critical value x standard error)

From the given information, the estimate for the slope is 0.705 and the standard error is 0.048. The critical value can be found from a t-distribution table using the degrees of freedom, which is 10 - 2 = 8. For a 95% confidence interval, the critical value is approximately 2.306. Substituting these values into the formula, we get:

Lower bound: 0.705 - (2.306 x 0.048) = 0.588

Upper bound: 0.705 + (2.306 x 0.048) = 0.822

Therefore, the 95% confidence interval for the slope is (0.588, 0.822).

Answer 2

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)