Explain Confidence interval for the true proportion.
1. A quality control engineer is attentive in the mean length of sheet insulation being cut automatically by machine. The wanted length of the insulation is 12 feet. It is known that the standard deviation in the cutting length is 0.15 feet. A sample of 70 cut sheets produces a mean length of 12.14 feet. This sample will be utilized to obtain a 99% confidence interval for the mean length cut by machine.
a. The critical value to use in procurement the confidence interval is _______________
b. The confidence interval goes from ________ to ________.
c. Presume the engineer had decided to estimate the mean length to within 0.03 with 99% confidence. Then the sample size would be ________.
2. The president of a university is worried that the percentage of students who have cheated on an exam is higher than the 1% acceptable level. A confidential arbitrary sample of 1000 students from a population of 7000 revealed that 6 of them said that they had cheated on an exam during the last semester.
a. Explain what is the critical value for the 90% one-sided confidence interval for the proportion of students who had cheated on an exam during the last 12 months?
b. Explain what is the upper bound of the 90% one-sided confidence interval for the proportion of students who had cheated on an exam during the last 12 months?