Statistical Significance and Hypothesis Testing - Prof. Todd M. Swanson, Exams of Statistics

Download Statistical Significance and Hypothesis Testing - Prof. Todd M. Swanson and more Exams Statistics in PDF only on Docsity! Math 210 Test 3 November 21, 2006 Name__________________________________ Questions 1-4 are multiple choice. Circle the letter of the best response. [4 pts each] 1. A significance test is used to prevent a machine from under filling or overfilling quart bottles of oil. On the basis of a sample, the null hypothesis is rejected and the machine is shut down for inspection. A thorough examination reveals there is nothing wrong with the filling machine. From a statistical point of view: a) A Type II error was made. b) A Type I error was made. c) A correct decision was made. d) Both Type I and Type II errors were made. 2. A researcher was interested in comparing the salaries of female and male employees of a particular company. Independent random samples of female employees (sample 1) and male employees (sample 2) were taken to calculate the mean salary, in dollars per week, for each group. A 90% confidence interval for the difference, µ1 – µ2 between the mean weekly salary of all female employees and the mean weekly salary of all male employees was determined to be (-$110, $10). a) We know that 90% of female employees at this company make between $110 less and $10 more than the male employees. b) We know that 90% of all random samples done on the employees at this company will show that the average female salary is between $110 less and $10 more per week than the average male salary. c) We are 90% confident that a randomly selected female employee at this company makes between $110 less and $10 more per week than a randomly selected male employee. d) Based on these data, with 90% confidence, female employees at this company average between $110 less and $10 more per week than the male employees. 3. Suppose you are conducting a test of significance at the α = 0.05 level. You get a P-value of 0.01 and make the appropriate conclusion. What is the probability of making a type I error in this case? a) 0.01 b) 0.05 c) 0.95 d) 0.99 4. I conduct a significance test and find that I am able to conclude that the alternative hypothesis is true at a significance level of α = .05. I may also conclude: a) The test would also be significant at level α = .01 b) The test would also be significant at level α = .10 c) Both a) and b) are true. d) Neither a) nor b) are true. 5. Offspring of a certain fruit fly can have yellow or ebony bodies and normal or short wings. Genetic theory predicts these traits will appear in a ratio of 9:3:3:1. (9/16 of them will be yellow-normal, 3/16 will be yellow-short, 3/16 will be ebony-normal, and 1/16 will be ebony- short.) A researcher checks 100 such flies and finds the distribution of traits to be 59, 20, 11, and 10 respectively. [14 pts.] a) Assuming the frequencies of the traits were distributed according to genetic theory, what would those expected counts be? yellow-normal = _______, yellow-short = _______, ebony-normal = _______, ebony-short = _________ b) Test at the α = 0.05 level to determine if the body and wing traits of the flies are not distributed according to the genetic model. i) State the null and alternative hypotheses. ii) Find the test statistic and P-value. iii) State the conclusion in words. 6. In a study done here on campus, students were asked if they break parietals. It was found that 15 out of 40 female students answered yes and 22 out of 40 males answered yes. Find a 95% confidence interval for the difference in the proportions of Hope male students that break parietals and female students that break parietals (or at least say they do)? Assume these proportions are accurate and come from simple random samples. [10 pts.]