Answer:
The value of the test statistic is [tex]t = 2.67[/tex]
Step-by-step explanation:
The null hypothesis is:
[tex]H_{0} = 7.8[/tex]
The alternate hypotesis is:
[tex]H_{1} \neq 7.8[/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 = 8.2, \mu = 7.8, \sigma = 0.6, n = 16[/tex]
Then
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \frac{8.2 - 7.8}{\frac{0.6}{\sqrt{16}}}[/tex]
[tex]t = 2.67[/tex]
The value of the test statistic is [tex]t = 2.67[/tex]
