The following observations are on stopping distance (ft) of a particular truck at 20 mph under specified experimental conditions.32.1 30.7 31.5 30.4 31.0 31.9USE SALTThe report states that under these conditions, the maximum allowable stopping distance is 30. A normal probability plot validates the assumption that stopping distance is normally distributed.(a) Does the data suggest that true average stopping distance exceeds this maximum value? Test the appropriate hypotheses using a = 0.01.State the appropriate hypotheses.ⒸHo: μ = 30Ha: μ = 30ⒸHo: μ = 30H₂: μ = 30OH:μ#30Hg: μ 30Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)t = 4.76XP-value =0.0029What can you conclude?O Reject the null hypothesis. There is not sufficient evidence to conclude that the true average stopping distance does exceed 30 ft.● Reject the null hypothesis. There is sufficient evidence to conclude that the true average stopping distance does exceed 30 ft.O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true average stopping distance does exceed 30ft.O Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average stopping distance does exceed 30 ft. (b) Determine the probability of a type II error when α = 0.01, 0 = 0.65, and the actual value of μ is 31 (use either statistical software or Table A.17). (Round your answer to three decimal places.)B = 0.990XRepeat this for μ = 32. (Round your answer to three decimal places.)B = 0.990XYou may have found the complement of the desired probability.(c) Repeat (b) using σ = 0.80.Use μ = 31. (Round your answer to three decimal places.)B = 0.990XYou may have found the complement of the desired probability.Use μ = 32. (Round your answer to three decimal places.)B = 0.990XYou may have found the complement of the desired probability.Compare to the results of (b).O We saw ß decrease when o increased.Ⓒ We saw ß increase when o increased.(d) What is the smallest sample size necessary to have a = 0.01 and ß = 0.10 when μ = 31 and σ = 0.65? (Round your answer to the nearest whole number.)

Question

The following observations are on stopping distance (ft) of a particular truck at 20 mph under specified experimental conditions.32.1 30.7 31.5 30.4 31.0 31.9USE SALTThe report states that under these conditions, the maximum allowable stopping distance is 30. A normal probability plot validates the assumption that stopping distance is normally distributed.(a) Does the data suggest that true average stopping distance exceeds this maximum value? Test the appropriate hypotheses using a = 0.01.State the appropriate hypotheses.ⒸHo: μ = 30Ha: μ = 30ⒸHo: μ = 30H₂: μ = 30OH:μ#30Hg: μ < 30ⒸH₂: μ = 30Ha: μ > 30Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)t = 4.76XP-value =0.0029What can you conclude?O Reject the null hypothesis. There is not sufficient evidence to conclude that the true average stopping distance does exceed 30 ft.● Reject the null hypothesis. There is sufficient evidence to conclude that the true average stopping distance does exceed 30 ft.O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true average stopping distance does exceed 30ft.O Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average stopping distance does exceed 30 ft. (b) Determine the probability of a type II error when α = 0.01, 0 = 0.65, and the actual value of μ is 31 (use either statistical software or Table A.17). (Round your answer to three decimal places.)B = 0.990XRepeat this for μ = 32. (Round your answer to three decimal places.)B = 0.990XYou may have found the complement of the desired probability.(c) Repeat (b) using σ = 0.80.Use μ = 31. (Round your answer to three decimal places.)B = 0.990XYou may have found the complement of the desired probability.Use μ = 32. (Round your answer to three decimal places.)B = 0.990XYou may have found the complement of the desired probability.Compare to the results of (b).O We saw ß decrease when o increased.Ⓒ We saw ß increase when o increased.(d) What is the smallest sample size necessary to have a = 0.01 and ß = 0.10 when μ = 31 and σ = 0.65? (Round your answer to the nearest whole number.)

Accepted Answer

Let μ denote the true average stopping distance.
The true average stopping distance is given as μ =…