problem 1:
a) A manufacturer claims that at least 95% of the equipment which he supplies to a factory conforms to specifications. An examination of a sample of 200 pieces of the equipment revealed that 18 were faulty. Test his claim at a significant level of 0.05.
b) In a random sample of 1000 persons from town A, 400 are found to be consumers of wheat. In a sample of 800 from town B, 400 are found to be consumers of wheat. Do such data reveal a significant difference between town A and town B, so far as the proportion of wheat consumers is concerned?
problem 2:
a) A manufacturer claims at least 95% of the equipment which he supplied to a factory confirmed for specifications. An examination of sample of 200 pieces of equipment revealed that 18 were faulty. Test his claim at 5% level of significance.
b) In a random sample of 160 workers exposed to a certain amount of radiation,24 experienced some ill effects. Construct 95% confidence interval for the true percentage.
problem 3:
a) In a large city 12 out of a random sample of 400 men were found to be drunkards. After the heavy increase in tax on intoxicants another random sample of 200 men in the same city included 8 drunkards. Was the observation decrease in the proportion of drunkards, after the increase of tax.
b) The owner of a machine shop must decide which of two snack vending machines to install in his shop. If each machine is tested 250 times, the first machine fails to work 13 times and the second machine fails to work 7 times test at the .05 level of significance whether the difference between the corresponding sample proportions is significant.
problem 4:
a) A study shows that 16 of 200 Tractor’s produced on one assembly line required extensive adjustments before they could be shipped, while the same was true for 14 of 400 tractors produced on another assembly line. At the .01 level of significance, does this support the claim that the second production line does superior work.
b) In a random sample of 1000 persons from town A, 400 are found to be consumers of wheat. In a sample of 800 from town B, 400 are found to be consumers of wheat. Do these data reveal a significant difference between town A and town B, so far as the proportion of wheat consumers is concerned?