Answer to Question #287803 in Statistics and Probability for xai

Question

An electrical firm manufactures light bulbs that have a length life of that is approximately normally distributed with a mean of 800 hours and a standard deviation of 40 hours. Test the hypothesis that 𝜇 = 800 ℎ𝑜𝑢𝑟𝑠 against the alternative μ ≠ 800 hours if random sample of 30 bulbs has an average life of 788 hours. Use a 0.01

Answer 1

$H_0: \mu = 800 \\ H_1: \mu ≠ 800 \\ n = 30 \\ \sigma = 40 \\ \bar{x} = 788 \\ α = 0.01$

Test-statistic

$Z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} \\ Z = \frac{788 -800}{40 / \sqrt{30}} = -1.643$

Two-tailed test.

Reject H₀ is Z ≤ -2.575 or Z≥ 2.575.

Since Z = -1.643 exceeds -2.575, reject the null hypothesis at the 1 % significance level.

We can conclude that $\mu ≠ 800$ .