An independent consumer group published its finding that the lifetimes of electric bulbs manufactured by BIG Corporation are approximately normally distributed with a mean of 700 days and a variance of 14,641 . BIG Corporation claims that the variance of its electric bulbs is less than 14,641. Suppose that we want to carry out a hypothesis test to see if BIG Corporation's claim is correct. State the null hypothesis $H_{0}$ and the alternative hypothesis $H_{1}$ that we would use for this test.
\[
\begin{array}{l}
H_{0}: \square \\
H_{1}: \square
\end{array}
\]
Answer
$H_{1}$: The variance of the lifetimes of electric bulbs manufactured by BIG Corporation is less than 14,641.
Step 1 ：State the null hypothesis $H_{0}$ and the alternative hypothesis $H_{1}$ for the test.
Step 2 ：$H_{0}$: The variance of the lifetimes of electric bulbs manufactured by BIG Corporation is 14,641.
Step 3 ：$H_{1}$: The variance of the lifetimes of electric bulbs manufactured by BIG Corporation is less than 14,641.
