Preliminary Data Analyses Indicate That It Is Reasonable to Use $\bar { x } = 810$

Essay

Preliminary data analyses indicate that it is reasonable to use a t-test to carry out the specified hypothesis test. Performthe t-test using the P-value approach.
-DuraBurn claims that the mean lifetime of its SuperGlo light bulbs is 904 hours. A researcher wants to perform a hypothesis test to determine whether the mean lifetime is actually less than this. A random sample of 10 DuraBurn SuperGlo bulbs exhibited an average lifetime $\bar { x } = 810$ hours with a standard deviation $s = 158$ hours. Using the hypotheses

$\begin{array} { l } \mathrm { H } _ { 0 } : \mu = 904 \\ \mathrm { H } _ { \mathrm { a } } : \mu < 904 \end{array}$

compute the value of the test statistic, and find the P-value for the sample. State your conclusion. Use a significance level of 0.05.