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A manufacturer claims that the mean lifetime, μ, of its light bulbs is 45 months. The standard deviation of these lifetimes is 9 months. 27 bulbs are selected at random, and their mean lifetime is found to be 40 months. Assume that the population is normally distributed. Can we conclude, at the 0.01 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 45 months? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis and the alternative hypothesis H₁. HO H₁:0 (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Can we conclude that the mean lifetime of light bulbs made by this manufacturer differs from 45 months? O Yes O No F Ix 0#0 a X S 0=0 OSO 90 Р ê 5 nin ロマロ OO

A manufacturer claims that the mean lifetime, μ, of its light bulbs is 45 months. The standard deviation of these lifetimes is 9 months. 27 bulbs are selected at random, and their mean lifetime is found to be 40 months. Assume that the population is normally distributed. Can we conclude, at the 0.01 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 45 months? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis and the alternative hypothesis H₁. HO H₁:0 (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Can we conclude that the mean lifetime of light bulbs made by this manufacturer differs from 45 months? O Yes O No F Ix 0#0 a X S 0=0 OSO 90 Р ê 5 nin ロマロ OO

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 13PPS
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Manufacturer claims

A manufacturer claims that the mean lifetime, μ, of its light bulbs is 45 months. The standard deviation of these lifetimes is 9 months. 27 bulbs are selected at random, and their mean lifetime is found to be 40 months. Assume that the population is normally distributed. Can we conclude, at the 0.01 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 45 months? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis and the alternative hypothesis H₁. HO H₁:0 (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Can we conclude that the mean lifetime of light bulbs made by this manufacturer differs from 45 months? O Yes O No H Ix X 0 ☐ 0#0 a X S 00 0=0 OSO 020 O<O Р <Q Ś O<O
Transcribed Image Text:A manufacturer claims that the mean lifetime, μ, of its light bulbs is 45 months. The standard deviation of these lifetimes is 9 months. 27 bulbs are selected at random, and their mean lifetime is found to be 40 months. Assume that the population is normally distributed. Can we conclude, at the 0.01 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 45 months? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis and the alternative hypothesis H₁. HO H₁:0 (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Can we conclude that the mean lifetime of light bulbs made by this manufacturer differs from 45 months? O Yes O No H Ix X 0 ☐ 0#0 a X S 00 0=0 OSO 020 O<O Р <Q Ś O<O
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