1. For a health screening in a large company, the diastolic and systolic blood pressures of all the employees were recorded. In a random sample of 150 employees, 12 were found to suffer from hypertension. Find 95% and 98% con?dence intervals for the proportion of the employees of this company with hypertension.
2. In a random sample of 500 items from a large lot of manufactured items, there were 40 defectives.
(a) Find a 90% con?dence interval for the true proportion of defectives in the lot.
(b) Is the assumption of normal approximation valid?
(c) Suppose we suspect that another lot has the same proportion of defectives as in the ?rst lot. What should be the sample size if we want to estimate the true proportion within 0.01 with 90% con?dence?