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

question 14

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.

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Definitions:

Abbreviation

A shortened form of a word or phrase used to simplify writing and speaking.

Peripheral Nervous System

The portion of the nervous system that exists outside the brain and spinal cord, responsible for transmitting sensory information to the central nervous system and carrying motor commands to muscles and organs.

Pns

Abbreviation for Peripheral Nervous System, which includes nerves and ganglia outside of the brain and spinal cord.

Transient Ischemic Attack

Often called a mini-stroke, a transient episode of neurological dysfunction caused by the loss of blood flow to the brain, spinal cord, or retina, without acute infarction.