APPLIED STATISTICS

1. In a study to determine whether the salaries of workers with college degrees are higher than the salaries of workers without college degrees on average, the p-value was found to be 0.002. (1) Define the population parameters of interest and write down the null and alternative hypotheses. (2) Using  = 0.05, are the results statistically significant? Why? (3) Give a formal conclusion about H0. (4) Give a conclusion in the context of the problem. (5) What type error we may make in this test? Describe the error. 2. A survey designed to obtain information on p = the proportion of registered voters who are in favor of a constitutional amendment requiring a balanced budget results in a sample of size n = 400. Of the 400 voters sampled 272 are in favor of a constitutional amendment requiring a balanced budget. We want to test to determine whether the majority of registered voters favor the constitutional amendment. (1) Write down the null and alternative hypotheses. (2) Use StatKey to create a randomization distribution and use it to calculate p-value for the test. (3) Using  = 0.05, are the results statistically significant? Why? (4) Give a formal conclusion about H0. (5) Give a conclusion in the context of the problem. (6) Use StatKey to construct a 95% confidence interval for p by the percentile method and interpret the confidence interval. (7) What is your conclusion based on the confidence interval. Is it consistent with your conclusion in the hypothesis test? (8) Construct a 95% confidence interval for p by the standard error method and compare it with the confidence interval by the percentile method. 3. In a study of the effect of smoking on lung cancer, 500 people were randomly selected and observed. The table below summarizes the data obtained in the study. Lung cancer No lung cancer Smoker 10 190 Nonsmoker 3 297 Let p1 denote the proportion of smokers who contract lung cancer and p2 denote the proportion of nonsmokers who contract lung cancer. We want to test to determine whether smoking increases the risk of lung cancer. (1) Write down the null and alternative hypotheses. (2) Use StatKey to create a randomization distribution and use it to calculate p-value for the test. (3) Using  = 0.05, are the results statistically significant? Why? (4) Give a formal conclusion about H0. (5) Give a conclusion in the context of the problem. (6) Use StatKey to construct a 99% confidence interval for p1 – p2 by the percentile method and interpret the confidence interval. (7) What is your conclusion based on the confidence interval. Is it consistent with your conclusion in the hypothesis test? 4. The department of natural resources reports that a fish is unsafe to eat if the polychlorinated biphenol (PCB) concentration exceeds 4.0 parts per billion (ppb). 10 fish were taken randomly from a local lake and the value of the PCB concentration for each fish was measured. The data are listed below. 2.9 7.6 4.8 5.2 5.1 4.7 6.9 4.9 3.7 3.8 Let  = the true mean value of the PCB concentration for all the fish in the lake. We want to test to determine whether the fish from this lake should not be eaten. (1) Write down the null and alternative hypotheses. (2) Use StatKey to create a randomization distribution and use it to calculate p-value for the test. (3) Using  = 0.05, are the results statistically significant? Why? (4) Give a formal conclusion about H0. (5) Give a conclusion in the context of the problem. (6) Use StatKey to construct a 90% confidence interval for  by the percentile method and interpret the confidence interval. (7) What is your conclusion based on the confidence interval. Is it consistent with your conclusion in the hypothesis test?