Question

A company advertises that its cans of caviar each contain 100 g of their product. A consumer advocacy group doubts this claim, and they obtain a random sample of 8 cans to test if the mean weight is significantly lower than 100 g. They calculate a sample mean weight of 99 g and a sample standard deviation of 0.9 g. The advocacy group wants to use these sample data to conduct a t-test on the mean. Assume that all conditions for inference have been met.
Provide the correct test statistic formula for their significance test.

Answer 1

Answer:

The value of the test statistic is -3.14.

Step-by-step explanation:

Test statistic:

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the expected value, $\sigma$ 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 $\mu = 100$

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 $X = 99, \sigma = 0.9, n = 8$

So the test statistic will be given by:

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$t = \frac{99 - 100}{\frac{0.9}{\sqrt{8}}}$

$t = -3.14$

The value of the test statistic is -3.14.