We need to compare the brakes of two vehicle makers. A random sample of 31 vehicles for each of the two brands were tested. The experiment to determine the brake quality was to obtain the time taken to slow down from 60 mph to 0 mph. The next results were observed: 1. Brand A: mean 78.667 s / variance 68 s2 2. Brand A: mean 72.667 s / variance 58 s2 Assume that the distance is normally distributed and that both samples have the same variance. Propose a statistical model to analyze this data and conclude if the stop distance is different for each brand (assume α =0.05).
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The braking ability of two types of automobiles was compared. Random samples of 64 automobiles were tested for each type. The recorded measurement was the distance required to stop when the brakes were applied at 40 miles per hour. The computed sample means and variances were as follows: $$\begin{array}{ll} \bar{y}_{1}=118, & \bar{y}_{2}=109 \\ s_{1}^{2}=102, & s_{2}^{2}=87 \end{array}$$ Do the data provide sufficient evidence to indicate a difference in the mean stopping distances of the two types of automobiles? Give the attained significance level.
Hypothesis Testing
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To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is 43 feet. Assume the population standard deviation is 4.6 feet. The mean braking distance for Make B is 46 feet. Assume the population standard deviation is 4.5 feet. At α=0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles? Assume the samples are random and independent, and the populations are normally distributed. The critical value(s) is/are Find the standardized test statistic z for μ1 - μ2.
David N.
A tire manufacturer tested the braking performance of one of its tire models on a test track. The company tried the tires on 10 different cars, recording the stopping distance for each car on both wet and dry pavement. Results are shown in the table. (TABLE CAN'T COPY) a) Write a 95$\%$ confidence interval for the mean dry pavement stopping distance. Be sure to check the appropriate assumptions and conditions, and explain what your interval means. b) Write a 95$\%$ confidence interval for the mean increase in stopping distance on wet pavement. Be sure to check the appropriate assumptions and conditions, and explain what your interval means.
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