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

The value of the test statistic is -3.14.

Explanation:

Test statistic:

`t = (X - \mu)/((\sigma)/(√(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 = (X - \mu)/((\sigma)/(√(n)))`

`t = (99 - 100)/((0.9)/(√(8)))`

`t = -3.14`

The value of the test statistic is -3.14.