Q1) Manufacturer of mechanical widgets claims that his widgets have the average useful life of= 8,000 hours of continuous use before failure. Independent testing organization caries out a life test on a random sample of 225 of manufacturer's widgets. Sample results differ between 6000 and 9200 hours though sample mean useful life of that sample is 6235 hours with the standard deviation of 600 hours. By using a 1% significance level, test manufacturer claim against alternative that true mean useful life is less than  8000 hours.

Q2) Sociolinguist claims that at least 45% of all college graduates are functionally illiterate (according to well known accepted standards). Random sample of 500 college graduates is chosen and subjected to standard literacy test. Results point out that 212 are, actually, functionally illiterate. Does this result support original claim, or is population percentage considerably less than 45%. Use alpha=.05 for level of significance.