Answer to Question #287803 in Statistics and Probability for xai

Question #287803

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 πœ‡ = 800 β„Žπ‘œπ‘’π‘Ÿπ‘  against the alternative ΞΌ β‰  800 hours if random sample of 30 bulbs has an average life of 788 hours. Use a 0.01


1
Expert's answer
2022-01-18T13:46:41-0500

"H_0: \\mu = 800 \\\\\n\nH_1: \\mu \u2260 800 \\\\\n\nn = 30 \\\\\n\n\\sigma = 40 \\\\\n\n\\bar{x} = 788 \\\\\n\n\u03b1 = 0.01"

Test-statistic

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

Two-tailed test.

Reject H0 is Z ≀ -2.575 or Zβ‰₯ 2.575.

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

We can conclude that "\\mu \u2260 800" .


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment