1. The mean output of an amplifier is 181 watts. It has σ = 10 watts. If 98 amplifiers are sampled, what is the probability that the average output is between 178.9 and 183.1 watts?
2. Suppose that 56% of students at a university are in the College of Business. A sample of 803 students is taken. What is the probability that the sample proportion of students in the College of Business is greater than 53%?
3. Given a confidence interval for a population mean of 11.78 < µ < 21.96, determine the original point estimate for the interval and the margin of error.
4. A chemist would like a margin of error for his experiment on chemical viscosity to be no more than 0.6217. How large a sample must he use if σ = 0.858 and he would like to have a 95% confidence level?
5. When must a critical t value be used rather than a critical z value?
6. The average GPA for a sample of 100 high school students considering attending a local university is 3.21 with s = 0.17. Determine a 99% confidence interval for the population mean. Interpret the interval.
7. The following is a random sample of the annual salaries of high school counselors in the US. Assuming that the distribution of salaries is approximately normal, construct a 90% confidence interval for the mean salary of high school counselors across the US. Interpret the interval.
$51,050
$38,740
$65,360
$42,640
$55,340
$32,980
$49,540
8. Case studies show that out of 10,351 convicts who escaped from US prisons, only 7867 were recaptured. Let p represent the proportions of all escaped convicts who will eventually be recaptured. Find a point estimate for p. Find a 99% confidence interval for p. Interpret the interval.
9. Samples of diameters taken from 11 gaskets off an assembly line are:
9.7, 10.6, 10.3 10.4, 9.9, 9.7, 10.1, 10.1, 10.4, 9.4 and 9.7
Build a 95% confidence interval for the population standard deviation. Please refer to the chi-square table.
10. Frozen Food Company uses a machine that packages blueberries in 7 pound portions. A sample of 30 packages has a variance of 0.1225 pounds. Construct a 90% confidence interval for the population variance. Please refer to the chi -square table.