Download Homework 5 - Hypothesis Testing - Introduction to Statistical Methods | MATH 363 and more Assignments Statistics in PDF only on Docsity! Assignment 5 - Hypothesis Testing Math 363 - April, 2009 1. During the 1980s, the general consensus is that about 5% of the nation’s children had autism. Some claimed that increases certain chemicals in the environment has led to an increase in autism. (a) Write an appropriate hypothesis test for this situation. (b) Give an appropriate test for this hypothesis, stating what are the necessary conditions for per- forming the test. (c) A recent study examined 384 children and found that 46 showed signs of autism. Perform a test of the hypothesis and state the p-value. (d) What are your conclusions? State how you use the p-value. 2. A company with a fleet of 150 cars found that the emission system of 7 our of the 22 cars tested failed to meet pollution guidelines. (a) Write a hypothesis to test if more than 20% of the entire fleet might be out of compliance. (b) Test the hypothesis based on the binomial distribution and report a p-value. (c) Is the test significant at the 10%, 5%, 1% level? 3. National data in the 1960s showed that about 44% of the adult population had never smoked. (a) State a null and alternative hypothesis to test that the fraction of the 1995 population of adults that had never smoked had increased. (b) A national random sample of 891 adults were interviewed and 463 stated that they had never smoked. Perform a z-test of the hypothesis and give an approriate p-value. (c) Create a 98% confidence interval for the proportion of adults who had never been smokers. (d) Give the value of the power function π(p) for p = 0.46, 0.48, 0.50, 0.52 with the choice of α = 0.02 and a “greater than” alternative hypothesis. (e) Compute the power function for these values if we increase the sample to 1600. Explain why these values increased. 4. One of the lenses in your supply is suspected to have a focal length f of 9cm rather than the 10cm claimed by the manufacturer. (a) Write an appropriate hypothesis test for this situation. (b) The focal length f is determined by using the thin lens formula, 1 s1 + 1 s2 = 1 f . 1
