STAT 200 Week 5 Homework - GRADE A

1. Why is a 99% confidence interval wider than a 95% confidence interval? 99% confidence interval is only slightly wider. In order to have a higher degree of confidence you need to include a larger proportion of the population. 2. A person claims to be able to predict the outcome of flipping a coin. This person is correct 16/25 times. Compute the 95% confidence interval on the proportion of times this person can predict coin flips correctly. What conclusion can you draw about this test of his ability to predict the future? .64±.1882= C.I. (.4518,.8282) 3. You take a sample of 22 from a population of test scores, and the mean of your sample is 60. (a) You know the standard deviation of the population is 10. What is the 99% confidence interval on the population mean? .60±.5.501= C.I. (54.499,65.501) (b) Now assume that you do not know the population standard deviation, but the standard deviation in your sample is 10. What is the 99% confidence interval on the mean now? .60±6.178= C.I. (53.822,66.178) 4. You were interested in how long the average psychology major at your college studies per night, so you asked 10 psychology majors to tell you the amount they study. They told you the following times: 2, 1.5, 3, 2, 3.5, 1, 0.5, 3, 2, 4. (a) Find the 95% confidence interval on the population mean. 2.25±.6538= C.I. (1.596,2.904) (b) Find the 90% confidence interval on the population mean. 2.25±.549= C.I. (1.701,2.799) 5. (100) What is meant by the term “90% confident” when constructing a confidence interval for a mean? a. If we took repeated samples, approximately 90% of the samples would produce the same confidence interval. b. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the sample mean. c. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean. d. If we took repeated samples, the sample mean would equal the population mean in approximately 90% of the sample 1 This study source was downloaded by from CourseH on :00:01 GMT -05:00 This study resource was shared via CourseH Oliver, Krystie Week 5 6. Suppose that a committee is studying whether or not there is waste of time in our judicial system. It is interested in the mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly surveyed 81 people who recently served as jurors. The sample mean wait time was eight hours with a sample standard deviation of four hours. a. i. x ¯ = 8 hours____ ii. sx = 4 hours____ iii. n= 81 iv. n– 1 = 80 b. Define the random variables X and X ¯ in words. X = # of hours wasted waiting to be called X ¯ = average # of hours of sample. c. Which distribution should you use for this problem? Explain your choice. Standard t-distro due to standard deviation of population = unknown. d. Construct a 95% confidence interval for the population mean time wasted. i. State the confidence interval. 8±0.8711= C.I. (7.129,8.871) ii. Sketch the graph. 95% 7.129 8.00 8.871 iii. Calculate the error bound. =1.96( 4 √ 81 ) = 0.88 e. Explain in a complete sentence what the confidence interval means. When 81 people are sampled 100x, it would be expected that 95% of the samples have averages within the interval.