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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 :

Answer:

The value of the test statistic is -3.14.

Step-by-step explanation:

Test statistic:

[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the expected value, [tex]\sigma[/tex] 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 [tex]\mu = 100[/tex]

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 [tex]X = 99, \sigma = 0.9, n = 8[/tex]

So the test statistic will be given by:

[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]t = \frac{99 - 100}{\frac{0.9}{\sqrt{8}}}[/tex]

[tex]t = -3.14[/tex]

The value of the test statistic is -3.14.

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