A manufacturer of a pasta sauce claims that there 471mg of sodium in a half-cup (125mL) of the sauce. To test this claim, a random sample 23 jars of pasta sauce are analyzed and a mean of 498.78mg of sodium is found with a standard deviation of 46.94mg. Assume the amount of sodium follows a normal distribution.
-How would you define the rejection region for this test at ? = .001?

Question

Quizplus · Accepted Answer

The rejection region is defined as extreme values of the test statistic that would only occur with a very low probability (less than the chosen significance level alpha). For a two-tailed test with alpha = .001, the rejection region would be split into two equal parts at the upper and lower tails of the t-distribution. Using a t-table with 99 degrees of freedom, we can find that the critical value for alpha/2 = .0005 (half of the .001 significance level) is 3.505. Therefore, any calculated t-value that falls outside of the range t > 3.505 or t < -3.505 would be in the rejection region. Among the answer choices, only Option C includes the correct critical value of 3.505, so it is the best choice.

A Manufacturer of a Pasta Sauce Claims That There 471mg