help me with this ap stat frq

6. A pharmaceutical company makes an antibiotic that has been shown to be effective at lowering bacteria in severe cases of pneumonia. However, since the antibiotic also causes stomach irritation in some patients, the company has created a new formula that it hopes will reduce that side effect. To see if the new formula reduces the incidence of stomach irritation for users of the antibiotic, the company conducted a small study to compare the new formula with the current antibiotic. In the study of 100 subjects with pneumonia, 50 were randomly assigned to take the current antibiotic and 50 were randomly assigned to take the new formula. Patient reactions at the end of the study are summarized in the table below. Patient Response Current antibiotic New Formula Total Had stomach irritation 21 17 38 Had no stomach irritation 29 33 62 Total 50 50 100 (a) Do the data from the study indicate, at the 10 percent level of significance, that the new formula helps to reduce the proportion of patients with stomach irritation compared to the current antibiotic? (The conditions for inference have been checked and verified.) (b) Based on your conclusion in part (a), which type of error, Type I or Type II, is possible? Describe the consequences of each error in the context of this study. (c) After the initial study, one of the researchers thought that the procedure described above would have more statistical power if the sample size was increased and suggested that a simulation study be run to test that theory. For the simulation, the researcher assumed that 40% of the subjects on the current antibiotic will have stomach irritation and that only 30% of the patients on the new formula will have stomach irritation. In addition, the total sample size will now be 200, with 100 subjects randomly assigned to each treatment. One-hundred trials of the simulation were conducted, and a p-value was calculated for each trial based on the testing procedure, significance level, and hypotheses used in part (a). A histogram of the p-values is given below. 50 40 30 Frequency of p-value 20 10- 0.0 O. 1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10 p-value Use the data in the histogram above to give an estimate for the power of the test if the test is performed at the 0.10 level of significance. Explain how you obtained your estimate. (d) Explain, in the context of this study, what the value obtained in part (c) represents