Fundamentals of Probability and Statistics for Engineers

Similarly, significance tests about the value of can be easily carried out with
use of as the test statistic.
An important special case of the above is the test of H 0 : 0 against
H 1 : 0. This particular situation corresponds essentially to the significance
test of linear regression. Accepting H 0 is equivalent to concluding that there is
no reason to accept a linear relationship between E Y and x at a specified
significance level. In many cases, this may indicate the lack of a causal
relationship between E Y and independent variable x.

Example 11.5.Problem: it is speculated that the starting salary of a clerk is a
function of the clerk’s height. Assume that salary (Y) is normally distributed and
its mean is linearly related to height (x); use the data given in Table 11.3 to test
the assumption that E Y and x are linearly related at the 5% significance level.

Answer: in this case, we wish to test H 0 : 0 against H 1 0,with 0:05.

F rom the data in Table 11.3, we have

According to Equation (11.44), we have

Table 11. 3 Salary, y (in $10 000), with height, x (in feet),

for Example 11.5

x 5.7 5.7 5.7 5.7 6.1 6.1 6.1 6.1

y 2.25 2.10 1.90 1.95 2.40 1.95 2.10 2.25

Linear Models and Linear Regression 353

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