Chapter 8 and 9 Review

  1. You want to compute a 99% confidence interval for a population mean. If the population standard deviation is 12 and the sample size is 40, find the value of z*.
  1. Which is wider… a 95% confidence interval or a 99% confidence interval or is it impossible to tell?
  1. In a test of H0: µ = 15 and Ha: µ ≠ 15, a sample size of 75 produces a z = 0.7 for the value of the test statistic. Find the p-value of the test.
  1. What is the difference between one-sample, matched pairs, and two-sample procedures? What is the difference between z and t procedures?
  1. Name two ways to increase the width of a confidence interval.
  1. If you want a 95% confidence interval and a margin of error 3 when you have a σ = 25, how many observations must you have?
  1. You want to compute a 98% confidence interval for the mean of a population with unknown standard deviation. The sample size is 20. What value of t* would you use?
  1. What are the conditions for hypothesis tests and confidence intervals for means?
  1. What is matched pairs?
  2. Police trainees were seated in a darkened room facing a projector screen. Ten different license planes were projected on the screen, one at a time, for 5 seconds each, separated by 15-second intervals. After the last 15-second interval, the lights were turned on and the police trainees were asked to write down as many of the 10 license plate numbers as possible, in any order at all. A random sample of 15 trainees who took this test where then given a week-long memory training course. They were then retested. The results are shown in the table below. Test, at the 5% level of significance, that the memory course improved the ability of the trainees to correctly identify license plates. D = before training – after training.

Plates identified correctly after training / Plates identified correctly before training
6 / 6
8 / 5
6 / 6
7 / 5
9 / 7
8 / 5
9 / 4
6 / 6
7 / 7
5 / 8
9 / 4
8 / 5
6 / 4
8 / 6
6 / 7
  1. The average height of a mature redbud tree is 25 ft. Mrs. Weakland has been trying to grow redbuds in the yard but has had some difficulty with this. She wants to know if her trees are growing to the average height. If not, she will add fertilizer to the trees. If they need fertilizer and she doesn’t use the fertilizer, the trees might die like the other ones she has planted. 
  • What is a type I error in this case?
  • What is a type II error in this case?
  • Which do you think would be worse and why?