Assignment -
Problems 1-4 below involve answering some statistical questions about data and writing mini-reports detailing your conclusions. Some (but not all) of the problems can be made easier by the use of SAS.
Your mini-reports should be typed in paragraph form and may include relevant graphs where appropriate. For each mini-report, the amount of actual text (not counting plots and graphs) certainly does not need to be more than one page in length. Some questions can be suitably answered with mini-reports substantially shorter than one page. Please do not include any computer code within your mini-reports. If you wish to include computer code, please put it in an appendix at the end of your document. If you want to include details of calculations (which is your choice ... it may or may not be helpful), it may be good to put those in an appendix as well rather than cluttering up the mini-reports.
NOTE: For all problems requiring inference, you can use α = 0.05 or 1 - α = 0.95 unless otherwise stated.
Problem 1: A scientist is interested in studying the weight of the larva of the Hercules beetle, found in Central and South America. The scientist takes a trip to the rainforest and gathers a sample of 22 specimens of Hercules beetle larvae. The scientist would like to obtain point and interval estimates of both the population mean weight and population standard deviation, for the population of Hercules beetle larvae. The data and some SAS code are given on the course website. Note that the sample mean is 114.727 grams and the sample standard deviation is 6.263. Write a mini-report describing a data analysis of your choice and your conclusions to answer the scientist's research questions.
Problem 2: A researcher wants the study the resting heart rates of three groups: nonsmokers, light smokers, and heavy smokers. He takes a sample of 14 nonsmokers, a sample of 14 light smokers, and a sample of 14 heavy smokers. Of interest is whether the mean resting heart rates are the same across the three populations. If the mean rates are different, the researcher would like some insight into which populations have different mean rates and the likely ordering of the population means. The data and some SAS code are given on the course website. Note that the sample mean heart rate for the nonsmokers was 60.193, with a sample standard deviation of 7.0005; the sample mean heart rate for the light smokers was 72.907, with a sample standard deviation of 5.263; the sample mean heart rate for the heavy smokers was 77.457, with a sample standard deviation of 6.269. Write a mini-report describing a data analysis of your choice and your conclusions to answer the research question.
Problem 3: An admissions officer at a Midwestern college is investigating the relationship between ACT math test score and college GPA. She is hoping to develop a model to predict college GPA using math ACT score. She has obtained a sample of 30 current students whose college GPA and math ACT scores are known. The data and some SAS code are given on the course website. The researcher would like to know whether a relationship exists between these two variables, what is the nature of the relationship, and whether math ACT is a useful predictor of college GPA. In particular, she knows of a potential admittee with a math ACT score of 23 whose GPA she wants to predict with a point prediction and a prediction interval. Develop a detailed analysis of these data addressing the officer's question and any other aspects of the data that you find relevant to the model. Write a mini-report describing your data analysis of choice and your conclusions to answer the research questions.
Problem 4: A study examined a potential relationship between the categorical variables: survival of coronary heart disease (CHD) patients, and pet ownership. The population of interest was all patients with CHD. A random sample of CHD patients was taken and each patient was classified according to (1) whether he or she survived for one year after diagnosis, and (2) whether he or she owned a pet. Of the patient who did not own a pet, 56 survived for at least one year, and 22 died within one year. Of the patients who owned a pet, 96 survived at least one year, and 16 died within one year. The question of interest is whether pet ownership is associated with survival, or whether they are independent. The researchers were also interested in learning whether pet ownership might actually improve survival chances. Write a mini-report describing a data analysis of your choice and your conclusions to answer the research questions.
Attachment:- Assignment Files.rar