Assignment 1 (50 marks in total)

1. (10 marks). A study used two different types of method to measure the oxygen delivery level of 25 patients. The file data1_Q1 .sav consists of two columns of data simulated to represent this information.
   1. What are the means, variances and standard deviations of ‘method1’ and ‘method2’ oxygen delivery level? (2 marks).
   2. Do box plots for ‘method1’ and ‘method2’. (2 marks).
   3. Do the Q-Q plots for ‘method1’ and ‘method2’. (2 marks).
   4. Produce 95% confidence intervals of the means for each method type (2 marks).
   5. Do the two confidence intervals (obtained from d) overlap? How would you interpret this result (2 marks)?
2. (5 marks) It is known, as a result of testing over many years, that the mean functional lifespan of an established dental operating lamp under normal working condition is 365 hours. A new lamp has recently come to the market, costing about 5% more, and a dental practitioner has tested 10 of them. He finds that the mean functional lifespan of these ten lamps is 380 hours, with an estimated standard deviation of 30.3 hours. Is it worth his while investing in the new lamps or should he stick with the old?
3. (10 marks) The number of patients visiting the dental departments of two District General Hospitals in a total of 14 equal sample time period is

Hospital A: 8 12 7 15 9 10 11 13 10 14 9 12 11 12

Hospital B: 11 6 8 12 7 6 9 10 8 10 7 12 11 12

We want to examine whether one department sees significantly more patients than the other.

1. Write down the null hypothesis and the alternative hypothesis. (2 marks)
2. Check the normality of the data. Are they normally distributed? (2 marks)
3. Assume the data is normally distributed, what test should we use? (1 marks)
4. Perform the statistical test of your choice, what is the observed difference between hospital A and hospital B? What the expected sampling variability? What is the ratio between the observed difference and the expected sampling variability? (3 marks).
5. What is the p-value? (1 mark)
6. What is your conclusion? (1 mark)

1. (10 marks). It is suspected that brushing teeth straight after eating a meal has a detrimental effect on enamel loss. To explore this theory, 15 pairs of twins performed two tests. One of the twins (twin 1) did tooth brushing 30 min after each meal, while the other twin (twin 2) brushed teeth straight after the meal. Measurement taken is the erosion of enamel (μm) after 12 months (compared with the baseline). The data are stored in the file data 1_Q4 .sav .
   1. Should we perform a paired sample t-test, or a two-sample independent t-test on the data set? (2 marks).
   2. Using the test of your choice, state the null hypothesis and the alternative hypothesis. (2 marks)
   3. Check the normality of the data (Hint: should we check the normality of enamel erosion of each twin, or should we check the normality of the difference between the enamel erosion of the twin pairs?) (2 marks)
   4. Assume the normality condition is satisfied, what is the statistical result of the test of your choice? (2 marks)
   5. What is your final conclusion? (How you interpret your finding to general public?) (2 marks)
2. (10 marks). Can quitting smoking improve oral health condition (which can be measure using Oral Health index) over 12 months? A team of researchers is planning a study to examine this question. Based on the results of a previous study, they are willing to assume a standard deviation of 2 for the percentage change in Oral Health index over the 12 month period. An increase in Oral Health index of 1 percent (effect size) would be considered clinically important. Assuming the data can be considered normally distributed, the researchers will conduct a two-sided test with a Type I error of 5% and are willing to accept a power of 0.80. (Hint: you can use the online Sample Size calculator provided in lecture 2, slide 49).

1. Perform a calculation to determine whether a sample of 30 subjects is a large enough sample to give the required power. (2 marks)
2. Estimate the smallest sample required to give a power of at least 0.9. (2 marks)
3. If Type I error is controlled as 0.01, and power needs to reach 0.9, what is the smallest sample size needed? (2 marks)
4. If I consider 2 percent of change in Oral Health index as clinical importance, given the required type I error as 5% and power as 0.8, what is the sample size needed? (2 marks)
5. How would you interpret the relation between sample size, significance level, power and effect size? (2 marks)

1. (5 marks). Reflective writing: Please comment on the statistical tests and data analysis techniques you learned from this module. (Minimum 1 sentence, maximum 100 words. You will be given 5 marks as long as you write something)

Price: $30.14

Solution: The downloadable solution consists of 14 pages, 1614 words and 14 charts.
Deliverable: Word Document