Answer:
The value of the test statistic is [tex]t = -1.44[/tex]
Step-by-step explanation:
The null hypothesis is:
[tex]H_{0} \geq 432[/tex]
The alternate hypotesis is:
[tex]H_{1} < 432[/tex]
Our test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
In this problem, we have that:
[tex]X = 426, \mu = 432, \sigma = 26, n = 39[/tex]
So
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \frac{426 - 432}{\frac{26}{\sqrt{39}}}[/tex]
[tex]t = -1.44[/tex]
The value of the test statistic is [tex]t = -1.44[/tex]
