Answer:
The value of the test statistic is -3.14.
Step-by-step explanation:
Test statistic:
![t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
In which X is the sample mean,
is the expected value,
is the standard deviation and n is the size of the sample.
A company advertises that its cans of caviar each contain 100 g of their product.
This means that ![\mu = 100](https://tex.z-dn.net/?f=%5Cmu%20%3D%20100)
They calculate a sample mean weight of 99 g and a sample standard deviation of 0.9 g. Sample of 8 cans.
This means that ![X = 99, \sigma = 0.9, n = 8](https://tex.z-dn.net/?f=X%20%3D%2099%2C%20%5Csigma%20%3D%200.9%2C%20n%20%3D%208)
So the test statistic will be given by:
![t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
![t = \frac{99 - 100}{\frac{0.9}{\sqrt{8}}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B99%20-%20100%7D%7B%5Cfrac%7B0.9%7D%7B%5Csqrt%7B8%7D%7D%7D)
![t = -3.14](https://tex.z-dn.net/?f=t%20%3D%20-3.14)
The value of the test statistic is -3.14.