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 31.9 Л USE SALT The 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 # 30 Η ι μ < 30 Ho: μ = 30 Ha μ> 30 ○ Ho: μ = 30 Haμ 30 Ho: μ # 30 H₂ μ = 30 Calculate 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 = P-value = What can you conclude? ○ Do not reject the null hypothesis. There is 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. ◇ Do not 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 not sufficient evidence to conclude that the true average stopping distance does exceed 30 ft. (b) Determine the probability of a type II error when a = 0.01, σ = 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 = Repeat this for μ = 32. (Round your answer to three decimal places.) ß = (c) Repeat (b) using σ = 0.80. Use 31. (Round your answer to three decimal places.) ß = Use = 32. (Round your answer to three decimal places.) ß = Compare to the results of (b). ○ We saw ẞ increase when σo increased. ○ We saw ẞ decrease when σ 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.)

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 31.9 Л USE SALT The 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 # 30 Η ι μ < 30 Ho: μ = 30 Ha μ> 30 ○ Ho: μ = 30 Haμ 30 Ho: μ # 30 H₂ μ = 30 Calculate 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 = P-value = What can you conclude? ○ Do not reject the null hypothesis. There is 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. ◇ Do not 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 not sufficient evidence to conclude that the true average stopping distance does exceed 30 ft. (b) Determine the probability of a type II error when a = 0.01, σ = 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 = Repeat this for μ = 32. (Round your answer to three decimal places.) ß = (c) Repeat (b) using σ = 0.80. Use 31. (Round your answer to three decimal places.) ß = Use = 32. (Round your answer to three decimal places.) ß = Compare to the results of (b). ○ We saw ẞ increase when σo increased. ○ We saw ẞ decrease when σ 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.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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