4. (10 points) A supplier of imported vernier calipers claims that 90% of their instruments have a precision of 0.999. Testing the null hypothesis p = 0.90 against the alternative hypothesis p 0.90, what can we conclude at the level of significance a = 0.10, if there were 645 calipers out of 700 with a precision of 0.999? 5. (10 points) An airline claims that only 6% of all lost luggage is never found. If, in a random sample, 17 of 200 pieces of lost luggage are not found, test the null hypothesis p = 0.06 against the alternative hypothesis p > 0.06 at the 0.05 level of significance. 6. (30 points) As a check on the quality of eye glasses purchased over the internet, glasses were individually ordered from several different online vendors. Among the 92 lenses with antireflection coating, 61 prescriptions required a thickness at the center greater than 1.9 mm and 31 were thinner. Of the 61 thicker lenses, 12 failed impact testing while 18 of the 31 thinner lens failed. (a) (15 points) Can we conclude, at the 0.05 level of significance, that a larger proportion of the thicker lenses will survive the impact test? (b) (15 points) Find a large sample 95% confidence interval for the true difference of probabilities