A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the $\sigma = 3.3$ mg claimed by the manufacturer. A) $ \mathrm { H } _ { 0 } : \sigma \neq 3.3 \mathrm { mg } $ $\mathrm { H } _ { 1 } : \sigma = 3.3 \mathrm { mg } $ B) $\mathrm { H } _ { 0 } : \sigma \leq 3.3 \mathrm { mg } $ $ \mathrm { H } _ { 1 } : \sigma 3.3 \mathrm { mg } $ C)$\mathrm { H } _ { 0 } : \sigma \geq 3.3 \mathrm { mg } $ $ \mathrm { H } _ { 1 } : \sigma

Question

A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the $\sigma = 3.3$ mg claimed by the manufacturer. 
A) $ \mathrm { H } _ { 0 } : \sigma \neq 3.3 \mathrm { mg } $
$\mathrm { H } _ { 1 } : \sigma = 3.3 \mathrm { mg } $

B) $\mathrm { H } _ { 0 } : \sigma \leq 3.3 \mathrm { mg }  $
$ \mathrm { H } _ { 1 } : \sigma > 3.3 \mathrm { mg } $

C)$\mathrm { H } _ { 0 } : \sigma \geq 3.3 \mathrm { mg } $
$ \mathrm { H } _ { 1 } : \sigma < 3.3 \mathrm { mg } $

D) $\mathrm { H } _ { 0 } : \sigma = 3.3 \mathrm { mg } $
$\mathrm { H } _ { 1 } : \sigma \neq 3.3 \mathrm { mg } $

Quizplus · Accepted Answer

The null hypothesis should always be the claim made by the manufacturer or the status quo. In this case, the manufacturer claims that the standard deviation is 3.3 mg. Hence, the null hypothesis should be H0:σ=3.3 mg and the alternative hypothesis should be H1:σ≠3.3 mg. Therefore, the best choice is D.

A Researcher Claims That the Amounts of Acetaminophen in a Certain