Question

a light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 761 hours. a random sample of 24 light bulbs has a mean life of 733 hours. assume the population is normally distributed and the population standard deviation is 62 hours. at \\( \alpha = 0.02 \\), do you have enough evidence to reject the manufacturers claim? complete parts (a) through (e).
(a) identify the null hypothesis and alternative hypothesis.
\\( \bigcirc \\) a. \\( h _ { 0 } : \mu \geq 761 \\) (claim) \\( \bigcirc \\) b. \\( h _ { 0 } : \mu = 733 \\) \\( \bigcirc \\) c. \\( h _ { 0 } : \mu < 733 \\) (claim)
\\( h _ { a } : \mu < 761 \\) \\( h _ { a } : \mu \
eq 733 \\) (claim) \\( h _ { a } : \mu \geq 733 \\)
\\( \bigcirc \\) d. \\( h _ { 0 } : \mu \leq 733 \\) \\( \bigcirc \\) e. \\( h _ { 0 } : \mu > 761 \\) \\( \bigcirc \\) f. \\( h _ { 0 } : \mu \
eq 761 \\) (claim)
\\( h _ { a } : \mu > 733 \\) (claim) \\( h _ { a } : \mu \leq 761 \\) (claim) \\( h _ { a } : \mu = 761 \\)

Explanation:

The null hypothesis \(H_0\) is a statement of equality or a claim that we assume to be true. The alternative hypothesis \(H_a\) is a statement that contradicts \(H_0\). The manufacturer's claim is that the mean life of a light - bulb is at least 761 hours (\(\mu\geq761\)). This is the null hypothesis. The alternative hypothesis is the opposite of the null hypothesis for a one - tailed test (since we are testing against the claim of "at least"), so \(H_a:\mu < 761\).

Answer:

A. \(H_0:\mu\geq761\) (claim), \(H_a:\mu < 761\)