Question

Most canned albacore tuna (canned white) contains about 0.32 parts per million of mercury. Suppose a random sample of 100 cans of a particular brand has a sample average of 0.31 parts per million of mercury with a standard deviation of 0.04. At the 0.01 significance level, is there evidence to support the claim that this particular brand of albacore tuna has a different mercury level than the common level? State the null hypothesis in symbols and in a complete sentence.

Answer 1

As we are testing whether this particular brand of albacore tuna has a different mercury level than the common level, therefore the null and the alternate hypothesis here are given as:

The test statistic here is computed as:

As this is a two tailed test, for n - 1 = 99 degrees of freedom, the p-value is computed from the t distribution tables as:

p = 2P( t₉₉ < -2.5) = 2*0.007 = 0.014

As the p-value here is greater than 0.01 which is the level of significance, therefore the test is not significant and we cannot reject the null hypothesis here, therefore we have insufficient evidence here that this particular brand of albacore tuna has a different mercury level than the common level.