STA2300: Data Analysis

Internal Code: MAS2206 Question 1 (22 marks) A low level of HDL (high density lipoprotein) is associated with an increased risk of heart disease. It is known that 14% of women in the general population have a low HDL level. There is concern that the proportion of African American women (living in Virginia) with a low HDL level is higher than this. Use the information in the dataset diabetes16.sav to answer the following questions: (a) (2 mark) Using SPSS, calculate the proportion of African American women in the study who have a low HDL level (i.e. a high risk of heart disease). (b) (20 marks) Without using SPSS, determine whether there is evidence to support the theory that the proportion of African American women (living in Virginia) with a low HDL level is higher than 14%. Perform a hypothesis test to statistically justify your answer by completing the following: i. State the appropriate hypotheses (define any symbols used). ii. Check the conditions and assumptions for this test. iii. Calculate the test statistic for this test. iv. Calculate the P-value for this test. v. Interpret the P-value and write a meaningful conclusion in the context of this situation. Question 2 (22 marks) Use the information in the dataset diabetes16.sav to answer the following questions. You should use SPSS to calculate the sample statistics you will need to do this question, but for parts (b) and (c) you are required to do all other calculations by hand, using a calculator. (a) (7 marks) Check the appropriate conditions and assumptions needed to calculate either a confidence interval or hypothesis test in relation to the population mean weight of African American males in Virginia. Include an appropriate graph to support your answer. (b) (6 marks) Estimate the population mean weight of African American males in Virginia, using a 95% confidence interval (show all working). (c) (9 marks) From historical data, it is known that the mean weight of African American males is 90 kg. Perform a hypothesis test to see if there is evidence to support a suspicion that the mean weight of African American males in Virginia is different to this. In performing this test: i. State appropriate hypotheses (define any symbols used). ii. Calculate the value of a suitable test statistic for this test. iii. Calculate the P-value of this test. iv. Write a meaningful conclusion at the 5% level of significance. STA2300 Data Analysis S3, 16 3 Question 3 (24 marks) Use the information in the dataset diabetes16.sav to answer the following questions. You should use SPSS to calculate any sample statistics you will need to do this question, but for parts b(ii) and (c) you are required to do all other calculations by hand, using a calculator. Data was collected at two different locations in Virginia – Birmingham and Louisa. As a researcher you are interested to see whether there is a difference in mean glycosylated haemoglobin percentage between residents at the two locations. (a) (4 marks) Check the appropriate conditions and assumptions needed to perform a hypothesis test comparing the population mean glycosylated haemoglobin percentage for residents of the two locations. Include an appropriate graph to support your answer. (b) (14 marks) Using an appropriate statistical test, determine if, on average, there is a difference in glycosylated haemoglobin percentage between people living in Birmingham and those living in Louisa. In performing the test, include: i. State appropriate hypotheses, clearly defining all symbols. ii. Calculate a suitable test statistic (you can use the results from part (a) in this calculation. iii. Find the P-value of the test (and include the degrees of freedom). iv. Interpret the P-value and write a meaningful conclusion in the context of the question. v. Now use SPSS to check your results for this hypothesis test. Attach or copy and paste the relevant output from SPSS for this test to your assignment. vi. Briefly comment on how the test statistic and P-value from SPSS output are similar to or differ from your hand calculations. (c) (6 marks) Estimate, with 90% confidence, the population mean difference in glycosylated haemoglobin percentage between people living in Birmingham and those living in Louisa. Ensure you explain the confidence interval in the context of the question. STA2300 Data Analysis S3, 16 4 Question 4 (32 marks) Use the information in the dataset diabetes16.sav to answer the following questions. Diastolic blood pressure was measured at the beginning of the study (dia_bp_1) and then again four weeks later (dia_bp_2). As researcher you want to know, if, on average, the diastolic blood pressure after four weeks is less than the diastolic blood pressure at the time of entry into the study. (a) (16 marks) Use a parametric test to answer this question by completing the following (parts i. to v. are to be completed without the aid of SPSS, although summary statistics, i.e. mean and standard deviation, required for the test can be found using SPSS): i. State appropriate hypotheses (define any symbols used). ii. State (but do not check) the assumptions for carrying out this test. Describe the assumptions in the context of this question. iii. Calculate the value of a suitable test statistic for this test. iv. Calculate the P-value of this test. v. Interpret the P-value and describe the outcome of the test in the context of this question. vi. Now use SPSS to carry out the analysis. Copy and paste the relevant SPSS output to your assignment. Do these results agree with those found in part iv? (Hint: comment on the p- value). (b) (16 marks) Describe an alternative statistical test that could be used to answer this question. Include in your answer: i. the name of the test, ii. the conditions/assumptions required for this test (in the context of the question), iii. a definition of the test statistic that would need to be calculated to perform this test, iv. the relative advantages and/or disadvantages of this test compared with the test you conducted to answer part (a), v. the circumstances under which you would use this test in preference to the one used in part (a). vi. Now use SPSS to carry out the analysis. Copy and paste the relevant SPSS output into your assignment. vii. State and interpret the P-value from the SPSS output and describe the outcome of the test in the context of this question.