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Answer each question completely, and explain thoroughly, when asked. No calculations necessary when calculator functions are used. No need to check conditions, unless otherwise stated. 1. To test the effectiveness of a new drug designed to relieve flu symptoms, 200 patients were randomly selected and divided into two equal groups. The 100 patients in Group 1 were given a pill containing the drug while the 100 patients in Group 2 were given a placebo. After a short while, 62 of those taking the drug felt a beneficial effect, compared to 41 of the patients taking the placebo. a. Multiple choice: Choose the 95% confidence interval that would estimate the true difference in the proportion of people who felt an effect between the two groups. (Circle the correct answer.) b. Interpret your answer from part (a) using a complete sentence. 2. A study was conducted to determine if the average salaries of librarians from two neighboring states were different. A sample of 60 librarians from each state was randomly selected. The sample mean from state #1 was $39,100 with a standard deviation of $2300. The sample mean from state #2 was $40,500 with a standard deviation of $2100. Fill in the following pieces of a hypotheses test to see if the average salaries are different. Use . Hypotheses Test statistic: p-value: Conclusion 3. Grades for a certain high school math course are expected to be distributed as follows: A, 25%; B, 25%; C, 40%; D, 5%; F, 5%. For a randomly selected year, the final grades are given. a. Complete the following table with the expected counts. Grade Observed Expected A 42 B 36 C 60 D 8 F 14 b. A goodness-of-fit test is conducted to determine if the grade distribution of the math course is different than expected. The test statistic is calculated as . State the p-value and your conclusion. Use . p-value Conclusion 4. The contingency table below shows the results of a random sample of 200 registered voters that was conducted to see whether their opinions on a bill are related to their party affiliation. Party Opinion Approve Disapprove No Opinion Republican 42 20 14 Democrat 50 24 18 Other 10 16 6 a. Calculate the expected counts of each category, assuming there is no association between opinion and party affiliation. Party Opinion Approve Disapprove No Opinion Republican Democrat Other b. Are the conditions met to conduct a test for independence? Explain your answer. (Do not conduct the test.) Answer each question completely, and explain thoroughly, when asked. No calculations necessary when calculator functions are used. No need to check conditions, unless otherwise stated. 1. To test the effectiveness of a new drug designed to relieve flu symptoms, 200 patients were randomly selected and divided into two e qual groups. The 100 patients in Group 1 w ere given a pill containing the drug while the 100 patients in Group 2 w ere given a placebo. After a short while, 62 of those taking the drug felt a beneficial effect, compared to 41 of the patients taking the pl acebo. a . Multiple choice: Choose the 95% confidence interval that would e stimate the true difference in the proportion of people who felt an effect between the two groups. (Circle the correct answer.) ( 0 . 172 , 0 . 242 ) ( 0 . 075 , 0 . 345 ) ( - 0 . 277 , 0 . 047 ) ( 0 . 579 , 0 . 749 ) b . Interpret your answer from part (a) using a complete sentence. 2. A study was conducted to determine if the average salaries of librarians from two neighboring states were different . A sample of 60 librarians fro m each state was randomly selected. The sample mean from state #1 was $ 3 9,100 with a standard deviation of $2300. The sample mean from state #2 was $ 4 0,500 with a standard deviation of $2100. Fill in the following pieces of a hypotheses test to see if t he average salaries are different . Use ?? = 0 . 05 . Hypotheses Test statistic: p - value: Conclusion 3. Grades for a certain high school math course are expected to be distributed as follows : A, 25%; B, 25%; C, 40%; D, 5%; F, 5%. For a randomly selected year , the final grades are given . Answer each question completely, and explain thoroughly, when asked. No calculations necessary when calculator functions are used. No need to check conditions, unless otherwise stated. 1. To test the effectiveness of a new drug designed to relieve flu symptoms, 200 patients were randomly selected and divided into two equal groups. The 100 patients in Group 1 were given a pill containing the drug while the 100 patients in Group 2 were given a placebo. After a short while, 62 of those taking the drug felt a beneficial effect, compared to 41 of the patients taking the placebo. a. Multiple choice: Choose the 95% confidence interval that would estimate the true difference in the proportion of people who felt an effect between the two groups. (Circle the correct answer.) (0.172,0.242) (0.075,0.345) (-0.277,0.047) (0.579,0.749) b. Interpret your answer from part (a) using a complete sentence. 2. A study was conducted to determine if the average salaries of librarians from two neighboring states were different. A sample of 60 librarians from each state was randomly selected. The sample mean from state #1 was $39,100 with a standard deviation of $2300. The sample mean from state #2 was $40,500 with a standard deviation of $2100. Fill in the following pieces of a hypotheses test to see if the average salaries are different. Use ??=0.05. Hypotheses Test statistic: p-value: Conclusion 3. Grades for a certain high school math course are expected to be distributed as follows: A, 25%; B, 25%; C, 40%; D, 5%; F, 5%. For a randomly selected year, the final grades are given.