Almost all suspension bridges are designed to transfer the load to the suspension cables, which in turn tranfer the load to the ground via the support pillars. The tensile strength of a cable must conform to some strict safety codes. Not only the cables must have some specified average strength, they must also not have too much variability in their tensile strengths. Any batch of cables whose standard deviation in the tensile strength exceeds 5 units is considered unreliable and must be discarded. A supplier provided a batch of cables for the project, out of which tests were conducted on 16 randomly selected (SRS) cables. Their tensile strengths showed the variability (variance) to be 30.9 squared units. What should be the null and the alternative hypotheses? Should we reject the entire batch if our level of significance is a = 0.05? (The tensile strengths of cables could be assumed to have a normal distribution.) The following "answers" have been proposed. (a) The null hypothesis is o > 5 and the alternative hypothesis is o < 5. At a = 0.05 level of significance we should reject the null hypothesis. That is, the batch is not within the safety code specifications. (b) The null hypothesis is o > 5 and the alternative hypothesis is o < 5. At a = 0.05 level of significance we should not reject the null hypothesis. That is, the batch is not within the safety code specifications. (c) The null hypothesis is o< 5 and the alternative hypothesis is 6 > 5. At a = 0.05 level of significance we should not reject the null hypothesis. That is, the batch is not within the safety code specifications. (d) The null hypothesis is o < 5 and the alternative hypothesis is o > 5. At a = 0.05 level of significance we should not reject the null hypothesis. That is, the batch is within the safety code specifications. (e) None of the above. The correct answer is (a) (b) (c) (d) (e) N/A (Select One)

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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Two competing internet routers, A and B, are being compared for the transmission speeds they can achieve for a random selection of transmitted files. The company which produces router A claims that its transmission speed exceeds that of router B. To compare, 1000 randomly selected file transmissions are monitored for each router. The sample mean and sample standard deviation of the transmission speed for router A was determined to be 10.04 and 0.987 GB/sec, respectively, while the same parameters for router B were 8.972 and 1.032 GB/sec, respectively. a) Is it reasonable to assume that the true standard deviations are known? Why or why not? b) Construct a 95% confidence interval on the mean transmission speed for router A. c) Construct a 95% confidence interval on the mean transmission speed for router B. d) By constructing a 95% confidence interval on the difference between the means, would you say that the claim made by the company producing router A is reasonable?
An improved filling machine will always be less incosistent, in the amount in each box is still Normally distributed, and now has a standard deviation is .10 ounces. Where should the average be set to assure that 90% of the boxes sold contain at least 16.00 ounces when this new filling machine is used?
Cartons of juice are such that their volumes are normally distributed with a mean of 150 ml and a standard deviation of 5 ml. Given that 5% of cartons are rejected for containing too little juice, find the minimum volume, to the nearest ml, that a carton must contain if it is to be accepted

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