From a packet containing iron nails, 1000 iron nails were taken at random & out of them 100 were found defective. Estimate the percentage of defective iron nails in the packet & assign limits within which the percentage probably lies.
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(A)From a packet containing iron nails, 1000 iron nails were taken at random and out of them 100 were foundFrom a packet containing iron nails, 1000 iron nails were taken at random and out of them 100 were found defective. Estimate the percentage of defective iron nails in the packet and assign limits within which the percentage probably lies?
(b) A random sample of 200 measurements from an infinite population gave a mean value of 50 and a and astandard deviation of 9. Determine the 95% confidence interval for the mean value of the population.
(c) In a random sample of 64 mangoes taken from a large consignment, some were found to be bad. Deduce that the percentage of bad mangoes in the consignment almost certainly lies between 31.25 and 68.75 given that the standard error of the proportion of bad mangoes in the sample 1/16.
(D) A random sample of 900 members is found to have a mean of 4.45 cms. Can it be reasonably regarded asa sample from a large population whose mean is 5 cms and variance is 4 cms?
(E) It is claimed that Americans are 16 pounds overweight on average. To test this claim, 9 randomly selected individuals were examined and the average excess weight was found to be 18 pounds. At the 5% level of significance, is there a reason to believe the claim of 16 pounds to be in error?
(F) The foreman of a certain mining company has estimated the average quantity of ore extracted to be 34.6 tons per shift and the sample standard deviation to be 2.8 tons per shift, based upon a random selection of 6 shifts. Construct 95% as well as 98% confidence interval for the average quantity of ore extracted per shift?