Question

big corporation advertises that its light bulbs have a mean lifetime, $mu$, of 2800 hours. suppose we have good reason to believe that $mu$ is different from 2800 hours and decide to do a statistical test of the claim. we choose a random sample of light bulbs manufactured by big and find that the mean lifetime for this sample is 2640 hours and that the sample standard deviation of the lifetimes is 700 hours. based on this information, complete the parts below. (a) what are the null hypothesis $h_0$ and the alternative hypothesis $h_1$ that should be used for the test? $h_0$: $square$ $h_1$: $square$ (b) suppose that we decide not to reject the null hypothesis. what sort of error might we be making? select (c) suppose the true mean lifetime of bigs light bulbs is 2800 hours. fill in the blanks to describe a type i error. a type i error would be select the hypothesis that $mu$ is select select when, in fact, $mu$ is select

Explanation:

Step1: Define null and alternative hypotheses

The null hypothesis $H_0$ is the statement of no - effect or the status - quo. The alternative hypothesis $H_1$ is what we suspect to be true instead of the null hypothesis. Here, the company claims $\mu = 2800$ hours, and we suspect $\mu
eq2800$ hours. So, $H_0:\mu = 2800$ and $H_1:\mu
eq2800$.

Step2: Identify type of error when not rejecting null hypothesis

If we do not reject the null hypothesis, the possible error is a Type II error. A Type II error occurs when we fail to reject a false null hypothesis.

Step3: Define Type I error

A Type I error occurs when we reject a true null hypothesis. If the true mean lifetime of BIG's light - bulbs is 2800 hours (i.e., $H_0$ is true), a Type I error would be rejecting the hypothesis that $\mu = 2800$ when, in fact, $\mu = 2800$.

Answer:

(a) $H_0:\mu = 2800$, $H_1:\mu
eq2800$
(b) Type II error
(c) A Type I error would be rejecting the hypothesis that $\mu$ is equal to 2800 when, in fact, $\mu$ is equal to 2800.