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

Here , we use t-test taking level of significance

He we want to test ,

v/s

Test statistics is ,

Where ,

Sample Mean =

Population mean =

Sample Standard deviation =

Sample Size =

Thereofore ,

Now ,

Table value is ,

Decision Rule :

If     then we reject at 5% level of significance .

Here ,

And ,

Decision :

Since , ,We may reject at 5% level of significance .

Conclusion : We may conclude that , cans of caviar each contain 100 g of their product .