Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis. -A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the $\sigma = 3.3 \mathrm { mg }$ claimed by the manufacturer. A) $\begin{array}{l} \mathrm{H}_{0}: \sigma \leq 3.3 \mathrm{mg} \ \mathrm{H}_{1}: \sigma3.3 \mathrm{mg} \end{array}$ B) $\begin{array}{l} \mathrm{H}_{0}: \sigma=3.3 \mathrm{mg} \ \mathrm{H}_{1}: \sigma \neq 3.3 \mathrm{mg} \end{array}$ C) $\begin{array}{l} \mathrm{H}_{0}: \sigma \neq 3.3 \mathrm{mg} \ \mathrm{H}_{1}: \sigma=3.3 \mathrm{mg} \end{array}$ D) $\begin{array}{l} \mathrm{H}_{0}: \sigma \geq 3.3 \mathrm{mg} \ \mathrm{H}_{1}: \sigma

Question

Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis.
-A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the $\sigma = 3.3 \mathrm { mg }$ claimed by the manufacturer.
A) $\begin{array}{l}
\mathrm{H}_{0}: \sigma \leq 3.3 \mathrm{mg} \
\mathrm{H}_{1}: \sigma>3.3 \mathrm{mg}
\end{array}$

B) $\begin{array}{l}
\mathrm{H}_{0}: \sigma=3.3 \mathrm{mg} \
\mathrm{H}_{1}: \sigma \neq 3.3 \mathrm{mg}
\end{array}$

C) $\begin{array}{l}
\mathrm{H}_{0}: \sigma \neq 3.3 \mathrm{mg} \
\mathrm{H}_{1}: \sigma=3.3 \mathrm{mg}
\end{array}$

D) $\begin{array}{l}
\mathrm{H}_{0}: \sigma \geq 3.3 \mathrm{mg} \
\mathrm{H}_{1}: \sigma<3.3 \mathrm{mg}
\end{array}$

Quizplus · Accepted Answer

The null hypothesis ($H_0$) is typically a statement of no effect or no difference and is what the researcher seeks to test against an alternative hypothesis ($H_1$). Since the researcher claims a difference in standard deviation from $\sigma = 3.3 \mathrm{mg}$, the correct formulation is $H_0: \sigma = 3.3 \mathrm{mg}$ and $H_1: \sigma \neq 3.3 \mathrm{mg}$, indicating a two-sided test for equality versus difference.

Assume That the Data Has a Normal Distribution and the Number