A Quality Control technician is interested in the proportion of boxes with no defectives. Suppose the true proportion of boxes with no defectives in the warehouse was not known. Hence, a technician computed a 95% confidence interval for the true proportion p of boxes with no defects from the sample having 70 out of 90 with no defects. She found the margin of error (8.6%) to be too large for her satisfaction. Using the sample proportion from the above table, about how many more samples does she need to take to estimate p with 95% confidence and a margin of error one half the size of the margin of error found in her first sample?

b) A large warehouse is used to store boxes of insulin needles. Each box contains 100 needles. Information about the entire warehouse as well as a sample of the boxes is as follows.

Number of Defectives per box	Number of Boxes (in warehouse)	Number of Boxes (in sample)
0	1500	70
> 0	375	20

A Quality Control technician is interested in the proportion of boxes with no defectives. What are the values of the statistic and the parameter?

2)A major car manufacturer wants to test a new engine to determine whether it meets new air-population standards. The mean emission of all engines of this type must be less than 20 parts per million of carbon. Assume that the emissions are normally distributed withsigma = 3.0. Ten engines are tested at random and the emission levels in parts per million are listed below

15.6

16.2

22.5

20.5

16.4

19.4

16.6

17.9

12.7

13.9

Do the data supply sufficient evidence to allow the manufacturer to conclude that this type of engine meets the pollution standard at the significance level0.01. The null and alternative hypotheses are

mu = 20 vsmu < 20

The one-sample z statistic is