Task 1 (Section 11-1 6. Blood Types) A medical researcher wishes to see if hospital patients in a large hospital have the same blood type distribution as those in the general population. The distribution for the general population is as follows: type A, 20%; type B, 28%; type 0, 36%; and type AB = 16%. He selects a random sample of 50 patients and finds the following: 12 have type A blood, 8 have type B, 24 have type 0, and 6 have type AB blood. At a = 0.10, can it be concluded that the distribution is the same as that of the general population? Task 2 (Section 11-1. 8. On-Time Performance by Airlines) According to the Bureau of Transportation Statistics, on-time performance by the airlines is described as follows: Action On-time National Aviation System delay Aircraft arriving late Other (because of weather and other conditions) % of Time 70.8 8.2 9.0 12.0 Records of 200 randomly selected flights for a major airline company showed that 125 planes were on time; 40 were delayed because of weather, 10 because of a National Aviation System delay, and the rest because of arriving late. At = 0.05, do these results differ from the government's statistics? Source: www.transtats.bts.gov Task 3 (Section 11-2.8. Ethnicity and Movie Admissions) Are movie admissions related to ethnicity? A 2014 study indicated the following numbers of admissions (in thousands) for two different years. At the 0.05 significance level, can it be concluded that movie attendance by year depended on ethnicity? Caucasian 2013 724 Hispanic 335 2014 370 292 African American 174 152 Other 107 140 Source: MPAA Study. Task 4 (Section 11-2.10 Women in the Military) This table lists the numbers of officers and enlisted personnel for women in the military. At = 0.05, is there sufficient evidence to conclude that a relationship exists between rank and branch of the Armed Forces? Army Officers 10,791 Enlisted 62,491 Navy 7,816 42,750 Marine Corps 932 9,525 Air Force 11,819 54,344 Source: New York Times Almanac. Task 5 (Section 12-1.8 Sodium Contents of Foods) Perform a complete one-way ANOVA. If the null hypothesis is rejected, use either the Scheffe or Tukey test to see if there is a significant difference in the pairs of means. Assume all assumptions are met. The amount of sodium (in milligrams) in one serving for a random sample of three different kinds of foods is listed. At the 0.05 significance level, is there sufficient evidence to conclude that a difference in mean sodium amounts exists among condiments, cereals, and desserts? Condiments 270 Cereals 260 Desserts 100 130 220 180 230 290 250 180 290 250 80 200 300 70 320 360 200 140 300 160 Source: The Doctor's Pocket Calorie, Fat, and Carbohydrate Counter. Task 6 (Section 12-2.10 Sales for Leading Companies) Perform a complete one-way ANOVA. If the null hypothesis is rejected, use either the Scheff or Tukey test to see if there is a significant difference in the pairs of means. Assume all assumptions are met. The sales in millions of dollars for a year of a sample of leading companies are shown. At a = 0.01, is there a significant difference in the means? Chocolate Cereal Candy Coffee 578 311 261 320 106 185 264 109 302 249 125 689 237 173 Source: Information Resources, Inc. Task 7 (Section 12-2.12 Per-Pupil Expenditures) Perform a complete one-way ANOVA. If the null hypothesis is rejected, use either the Scheff or Tukey test to see if there is a significant difference in the pairs of means. Assume all assumptions are met. The expenditures (in dollars) per pupil for states in three sections of the country are listed. Using a = 0.05, can you conclude that there is a difference in means? Eastern Middle Western third third third 4946 6149 5282 5953 7451 8605 6202 6000 6528 7243 6479 6911 6113 Source: New York Times Almanac. Task 8 (Section 12-3. 10. Increasing Plant Growth) Assume that all variables are normally or approximately normally distributed, that the samples are independent, and that the population variances are equal. a. State the hypotheses. b. Find the critical value for each F-test. c. Complete the summary table and find the test value. d. Make the decision. e. Summarize the results. (Draw a graph of the cell means if necessary.) A gardening company is testing new ways to improve plant growth. Twelve plants are randomly selected and exposed to a combination of two factors: a "Grow-light" in two different strengths. a plant food supplement with different mineral supplements. After several days, the plants are measured for growth, and the results (in inches) are put into the appropriate boxes. Grow-light 1 Grow-light 2 Plant food A 9.2, 9.4, 8.9 8.5, 9.2, 8.9 Plant food B 7.1, 7.2, 8.5 5.5, 5.8, 7.6 Can an interaction between the two factors be concluded? Is there a difference in mean growth with respect to light? With respect to plant food? Use a = 0.05. Use R to complete the following steps. Be sure to include all code in an appendix at the end of your submission. Assume the expected frequencies are equal and = 0.05. Number the tasks as "Task 9.1", "Task 9.2", etc. 1. Download the file 'baseball.csv' from the course resources and import the file into R. 2. Perform EDA on the imported data set. Write a paragraph or two to describe the data set using descriptive statistics and plots. Are there any trends or anything of interest to discuss? 3. Assuming the expected frequencies are equal, perform a Chi-Square Goodness-of-Fit test to determine if there is a difference in the number of wins by decade. Be sure to include the following: a. State the hypotheses and identify the claim. b. Find the critical value ( = 0.05) (programmatically). c. Compute the test value. d. Make the decision. Clearly state if the null hypothesis should or should not be rejected and why. e. Does comparing the critical and test values provide the same result as comparing the p- value from R with the significance level? Here is some code to get you started. Be sure to import the dplyr and tidyverse packages. # Extract decade from year bb$Decade % summarize(wins sum(W)) %>% as.tibble() 4. Download the file 'crop_data.csv' from the course resources and import the file into R. 5. Perform a Two-way ANOVA test using yield as the dependent variable and fertilizer and density as the independent variables. Explain the results of the test. Is there reason to believe that fertilizer and density impact yield? ** Be sure to convert the variables density and fertilizer to R factors. ** Include a null and alternate hypothesis for both factors and the interaction.