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In order to control the quality of the compaction of the subgrade in a highway pavement project,200 soil specimens were prepared and tested. Twelve out of the sample of 200 specimens were found to have compaction below CBR requirement. Calculate the 99% confidence interval of the proportion of well compacted pavement.CONFIDENCE INTERVAL FOR VARIANCE

A machine is used to fill cement bags in an assembly line operation. Much concern centers around the variability in the number of kg of cement in the bag. The standard deviation in weight of product is known to be 0.3 kg. An improvement is implemented after which a random sample of 20 bags are selected and the sample variance is found to be 0.045 kg. Find a 95% confidence interval on the variance in the weight of the cement product.

Two kinds of rebars are being compared for strength. Fifty pieces of each type of rebars are tested under similar conditions. Brand A had an average: tensile strength of 78.3 kN with a standard deviation of 5.6 kN, while brand B had an average tensile strength of 87.2 kN with a standard deviation of 6.3 kN. Construct a 95% confidence interval for the difference of the population means.

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An experiment was conducted to determine whether surface finish has an effect on the endurance limit of steel. An existing theory says that polishing increases the average endurance limit (reverse bending). From a practical point of view, polishing should not have any effect on the standard deviation of the en- durance limit. An experiment was performed on 0.4% carbon steel using both unpolished and polished smooth-turned specimens. The data are as follows: Endurance Limit (psi) for: Polished Unpolished 0.4% Carbon 0.4% Carbon 85,500 91,900 89,400 84,000 89,900 78,700 87,500 83,100 82,600 82,400 81,700 79,500 79,400 69,800 79,900 83,400 Find a 95% confidence interval for the difference between the population means for the two methods, assuming that the populations are approximately normally distributed.

Ten engineering schools in the United States were surveyed. The sample contained 250 civil engineers, 80 being women; 175 environmental engineers, 40 being women. Compute a 90% confidence interval for the difference between the proportion of women in these two fields of engineering. Is there a significant difference between the two proportions?

Statistical HypothesisA statistical hypothesis is a statement about the parameters of one or more populations.May also be thought of as a statement about the probability distribution of a random variable.15Supposed that we want to determine whether the average content of colored cement bag is less than 12 lb.Hypothesis TestTrial by JuryCement bagaccusedResearcherprosecutionDataevidencesClaim: