Three different brands of automobile batteries, each one having a 42-month warranty, were included in a study of battery lifetime. A random sample of batteries of each brand was selected and lifetime (in months) was determined, resulting in the following data.Brand 145395247454143Brand 239445053484740Brand 350474348564448 State and test the appropriate hypotheses using a significance level of 0.05.State the appropriate null and alternative hypotheses. (Let ?1, ?2, and ?3 be the true mean lifetimes for the three brands.)H0 : all three of the ?i's are differentHa : ?1 = ?2 = ?3H0 : ?1 = ?2 = ?3Ha : all three of the ?i's are different H0 : ?1 = ?2 = ?3Ha : at least two of the three ?i's are differentH0 : ?1 ≠ ?2 ≠ ?3Ha : at least two of the three ?i's are the sameH0 : at least two of the three ?i's are differentHa : ?1 = ?2 = ?3Summarize your calculations in an ANOVA table. (Round your answers to two decimal places.)Source ofVariationdfSum ofSquaresMeanSquareFTreatments Error Total Use technology to find the P-value. (Round your answer to four decimal places.)P-value = What can you conclude?Reject H0. We do not have sufficient evidence to conclude that there is a difference between the three means.Fail to reject H0. We do not have sufficient evidence to conclude that there is a difference between the three means. Fail to reject H0. We have sufficient evidence to conclude that there is a difference between the three means.Reject H0. We have sufficient evidence to conclude that there is a difference between the three means.

Given, Brand 1 45 39 52 47 45 41 43 Brand 2 39 44 50 53…

Answered: Three different brands of automobile…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 58E: What is meant by the sample space of an experiment?

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Three different brands of automobile batteries, each one having a 42-month warranty, were included in a study of battery lifetime. A random sample of batteries of each brand was selected and lifetime (in months) was determined, resulting in the following data.

Brand 1	45	39	52	47	45	41	43
Brand 2	39	44	50	53	48	47	40
Brand 3	50	47	43	48	56	44	48

State and test the appropriate hypotheses using a significance level of 0.05.

State the appropriate null and alternative hypotheses. (Let ?₁, ?₂, and ?₃ be the true mean lifetimes for the three brands.)

H₀ : all three of the ?_i's are different
H_a : ?₁ = ?₂ = ?₃H₀ : ?₁ = ?₂ = ?₃
H_a : all three of the ?_i's are different H₀ : ?₁ = ?₂ = ?₃
H_a : at least two of the three ?_i's are differentH₀ : ?₁ ≠ ?₂ ≠ ?₃
H_a : at least two of the three ?_i's are the sameH₀ : at least two of the three ?_i's are different
H_a : ?₁ = ?₂ = ?₃

Summarize your calculations in an ANOVA table. (Round your answers to two decimal places.)

Source of Variation	df	Sum of Squares	Mean Square	F
Treatments
Error
Total

Use technology to find the P-value. (Round your answer to four decimal places.)

P-value =

What can you conclude?

Reject H₀. We do not have sufficient evidence to conclude that there is a difference between the three means.Fail to reject H₀. We do not have sufficient evidence to conclude that there is a difference between the three means. Fail to reject H₀. We have sufficient evidence to conclude that there is a difference between the three means.Reject H₀. We have sufficient evidence to conclude that there is a difference between the three means.

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