QuestionThe records show that the lifetimes of electric bulbs manufactured in the past by BIG Corporation have a mean of 9790 hours and a standard deviation of 124 . The corporation claims that the current standard deviation, $\sigma$, is less than 124 following some adjustments in its production unit. A random sample of 27 bulbs from the current production lot is examined by the corporation. The sample has a mean lifetime of 9795 hours, with a standard deviation of 90 . Assume that the lifetimes of the recently manufactured bulbs are approximately normally distributed, Is there enough evidence to conclude, at the 0.10 level of significance, that the corporation's claim is valid?
Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis $H_{0}$ and the alternative hypothesis $H_{1}$. $$\begin{array}{l} H_{0}: \square \\ H_{1}: \square \end{array}$$ (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) $\square$ (d) Find the critical value. (Round to three or more decimal places.) $\square$ (e) Can we support the claim that the current standard deviation of lifetimes of electric bulbs manufactured by the corporation is less than 124 ? Yes No