Answer:
The value of the test statistic is [tex]t = -2.09[/tex]
Step-by-step explanation:
The null hypothesis is:
[tex]H_{0} = 6.6[/tex]
The alternate hypotesis is:
[tex]H_{1} \neq 6.6[/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(square roof of the variance) and n is the size of the sample.
In this problem, we have that:
[tex]X = 6.5, \mu = 6.6, \sigma = \sqrt{0.64} = 0.8, n = 280[/tex]
So
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \frac{6.5 - 6.6}{\frac{0.8}{\sqrt{280}}}[/tex]
[tex]t = -2.09[/tex]
The value of the test statistic is [tex]t = -2.09[/tex]
