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**Q1:**1. DETAILS DEVORESTAT9 8.3.035.S. MY NOTES The article "Uncertainty Estimation in Railway Track Life-Cycle Cost"+ presented the following data on time to repair (min) a rail break in the high rail on a curved track of a certain railway line. 159 120 480 149 270 547 340 43 228 202 240 218 A normal probability plot of the data shows a reasonably linear pattern, so it is plausible that the population distribution of repair time is at least approximately normal. The sample mean and standard deviation are 249.7 and 145.1, respectively. (a) Is there compelling evidence for concluding that true average repair time exceeds 200 min? Carry out a test of hypotheses using a significance level of 0.05. State the appropriate hypotheses. ⒸM-200 H₁: <200 ⒸM-200 H₂>200 No 200 H₂-200 ⒸM-200 H: 200 ⒸM₂: > 200 MH-200 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) t= P-value= What can you conclude? There is compelling evidence that the true average repair time exceeds 200 min. There is not compelling evidence that the true average repair time exceeds 200 min. (b) Using a 150, what is the type II error probability of the test used in (a) when true average repair time is actually 300 min? That is, what is (300)? (Round your answer to two decimal places. You will need to use the appropriate table in the Appendix of Tables to answer this question.) A(300) - MacBook ProSee Answer**Q2:**6. DETAILS DEVORESTAT9 9.5.064. The following observations are on time (h) for an AA 1.5-volt alkaline battery to reach a 0.8 voltage. Brand A: 8.65 8.84 8.91 8.82 8.75 8.52 8.72 8.78 8.76 Brand B: 8.86 8.71 8.71 8.8 8.73 8.76 8.78 8.74 8.79 Normal probability plots support the assumption that the population distributions are normal. Does the data suggest that the variance of the Brand A population distribution differs from that of the Brand B population distribution? Test the relevant hypotheses using a significance level of 0.05. [Note: The two-sample t test for equality of population means gives a P-value of 0.733.] The Brand A batteries are much more expensive than the Brand B batteries. State the relevant hypotheses. (Use a, for Brand A batteries and a₂ for Brand B batteries.) ⒸH₂0₁ ¹0₂² ⒸH: 0²-0₂² M₂: 0,² > 0₂² H₁: 0 ₁ ² = 0₂² M₂:0₂ ² = 0₂² Calculate the test statistic. (Round your answer to two decimal places.) fm What can be said about the P-value for the test? ⒸP-value > 0.100 0.050 < P-value < 0.100 0.010 < P-value < 0.050 0.001 < P-value < 0.010 OP-value < 0.001 MY NOTES State the conclusion in the problem context. Reject H. The data suggests that there is difference in the population variances of the two battery brands./nⒸH₂:0₁ ²0₂ ² H₂: 0₂² 20₂² ⒸH₂:0₁²-0₂² Calculate the test statistic. (Round your answer to two decimal places.) f= What can be said about the P-value for the test? OP-value > 0.100 0.050 < P-value < 0.100 0.010 < P-value < 0.050 0.001 < P-value < 0.010 OP-value < 0.001 State the conclusion in the problem context. Reject Ho. The data suggests that there is difference in the population variances of the two battery brands. Fail to reject Ho. The data does not suggest that there is difference in the population variances of the two battery brands. Fail to reject Ho. The data suggests that there is difference in the population variances of the two battery brands. Reject Ho. The data does not suggest that there is difference in the population variances of the two battery brands. You may need to use the appropriate table in the Appendix of Tables to answer this question. Submit Answer Home My Assignments Request ExtensionSee Answer**Q3:**Question 1 The editor of a UK college magazine is checking the latest edition of the magazine before it goes to print, but they have found some problems. (a) Three stories each have a piece of data missing. The topics of the three stories are: Story 1: A science project to find the fastest reaction time when mixing certain chemicals. Story 2: An interview with the winner of the inter-collegiate 1500 metre race. Story 3: The results of a survey to find the average time it took students to travel from their home to the entrance of the college campus. The three pieces of data are: A: 5 minutes 33 seconds B: 42 minutes C: 31.4567 seconds Match each story with the most appropriate piece of data, justifying your answer. (b) A story about the campus shop says that students spend on average £4.5682351 per visit. The editor rightfully thinks that this level of accuracy is unjustified. Round £4.5682351 to an appropriate level of accuracy, justifying your answer. (c) The word counts for the main articles in the latest magazine edition are: 220, 470, 1300, 250, 1100, 540, 380, 670. (i) Calculate by hand the median word count. Show your working. (ii) Calculate by hand the range of word counts. Show your working. See Answer

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