Reference no: EM133138585
STA8170 Statistics for Quantitative Researchers - University of Southern Queensland
Question 1
Use the information in the dataset cardiac_22.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 (a) and (d) you are required to do the rest of the calculations by hand, using a calculator.
(a) Estimate the population mean heart rate for all critically ill patients who survived cardiac arrest after being admitted to hospital, using a 98% confidence interval by hand (show all working). You may use SPSS to find the summary statistics required for hand calculations, but the actual confidence interval must be calculated by hand. Make sure you ONLY select those patients who survived for this question.
(b) Check the appropriate conditions and assumptions needed for the validity of the confidence interval or hypothesis test for the population mean heart rate for all critically ill patients who survived cardiac arrest (include an appropriate graph to support your answer).
(c) The average heart rate of adults is usually no more than ninety beats per minute. In the study to identify risk factors associated with cardiac arrest, measurements of heart rate were taken for each of the 88 critically ill patients who survived cardiac arrest. State appropriate hypotheses (define any symbols used) to perform a hypothesis test to see if the mean heart rate for critically ill patients admitted to hospital in cardiac arrest who survived is higher than that of the overall population (regardless of whether the conditions in part (b) are satisfied).
(d) Calculate the value of a suitable test statistic for the test in part (c) by hand.
(e) Find the P-value of the test, based on the test statistic calculated in part (d), and write a meaningful conclusion in the context of the situation, at the 1% level of significance.
(f) Now, check your answers for parts (d) and (e) by finding the value of the test statistic and the P-value using SPSS. Include SPSS output in your answer and comment on the comparison with the hand calculated values. Explain any differences.
Question 2
Use the information in the dataset cardiac_22.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 (d)-(g) you are required to do the rest of the calculations by hand, using a calculator and statistical tables.
According to the researchers at the Cardiac Research Unit in California, historically 55% of all critically ill patients admitted to hospital in cardiac arrest survived. However, the researchers now believe that the proportion of critically ill patients who survive cardiac arrest after being admitted to hospital is no longer 55%.
(a) What is the variable of interest to the researchers?
(b) State the appropriate hypotheses (define any symbols used) to test the researchers' claim that the proportion of critically ill patients who survive cardiac arrest is no longer 55%.
(c) Check the conditions and assumptions for the test in part (b).
(d) Calculate the test statistic for the test in part (b).
(e) Find the P-value for the test in part (d) and write a meaningful conclusion in the context of this situation.
(f) If the researchers want to be 99% confident that the margin of error of the estimate of the true proportion of critically ill patients who survive cardiac arrest after being admitted to hospital is within 0.02, what minimum sample size is required? Use a conservative method in determining the sample size.
(g) The researchers decide that instead of using a conservative method (as required in part (f)), they will use information obtained from the cardiac_22.sav women only data to decide how many patients they would need to include in a follow-up study (keeping the same level of confidence and margin of error). What is the impact of this decision? (Include evidence to support your answer).
Question 3
Evidence suggests that non-smokers who live with smokers and are therefore exposed to sidestream smoke (as opposed to mainstream smoke, which is inhaled by the smoker directly from the cigarette) may have increased risk of lung disease. Mainstream and sidestream yields (in mg) of tar, nicotine, and carbon monoxide for eight nonfilter cigarettes appeared in the paper "Yields of Tar, Nicotine, and Carbon Monoxide in Sidestream Smoke of Canadian Cigarettes" (Amer. J. Public Health (1984):228{231).
Data on tar yield is given below.
|
Cigarette
|
Sidestream Yield
|
Mainstream Yield
|
|
1
|
15.8
|
18.5
|
|
2
|
16.9
|
17.0
|
|
3
|
21.6
|
17.2
|
|
4
|
18.8
|
19.4
|
|
5
|
29.3
|
15.6
|
|
6
|
20.7
|
16.4
|
|
7
|
18.9
|
13.3
|
|
8
|
25.0
|
10.2
|
Is there evidence that non-smokers who live with smokers have an increased risk of lung disease? In other words, is the mean yield (in mg) of tar, nicotine, and carbon monoxide greater in sidestream smoke than in mainstream smoke?
(a) State appropriate hypotheses (define any symbols used) to perform this test.
(b) State (but do not check) the assumptions for carrying out the test in (a). Describe the assumptions in the context of this question.
(c) Without using SPSS, calculate the value of a suitable test statistic for the test in (a). You can use SPSS for calculating appropriate sample statistics.
(d) Without using SPSS, find the degrees of freedom and P-value of the test.
(e) Interpret the P-value and describe the outcome of the test in the context of this question.
(f) Using SPSS calculate the value of the test statistic and P-value of the test and compare with those found in parts (c) and (d). You should include your SPSS output in your response.
Question 4
An evaluation of diffusion bonding of zircaloy components is performed. The main objective is to determine which of the four elements (nickel, iron, copper, and zinc) is the best bonding agent. The data in the following table shows the pressure (in units of 1000 pounds per square inch) required to separate the bondage of the components. Is there evidence of a difference in mean pressure required to separate the components among the four bonding agents?
|
Nickel
|
Iron
|
Copper
|
Zinc
|
|
67
|
72
|
72
|
65
|
|
68
|
69
|
66
|
63
|
|
76
|
83
|
75
|
65
|
|
73
|
78
|
67
|
68
|
|
66
|
74
|
|
67
|
|
76
|
|
|
|
For the above data, answer the following questions:
(a) Stating the parameters and explaining all symbols, write the one-way ANOVA model to represent the data.
(b) Write down all the assumptions of the one-way ANOVA model in the context of the problem.
(c) Stating the hypotheses for the problem, define the appropriate test statistic.
(d) Calculate the value of the Sum of Squares Total (Total SS), Sum of Squares
Treatment (SSTr) and Sum of Squares Error (SSE) for the data, and then find the value of the appropriate test statistic testing the hypotheses in part (c ). This question must be done by hand without using SPSS.
(e) Stating the degrees of freedom, find the P-value of the test.
(f) Comment on the outcome of the test in the context of the problem.
(g) Now use SPSS to perform one-way analysis of variance and comment on the outcome of the test, including the ANOVA table produced by SPSS.
Question 5
A large rent-a-car centre in Toowoomba recently purchased three brands of cars, each having three colours. The following data on the brand of the car and their associated colours are available.
|
|
Colour
|
|
Brand
|
|
Black
|
White
|
Red
|
Total
|
|
Toyota
|
25
|
20
|
10
|
55
|
|
Mazda
|
10
|
20
|
20
|
50
|
|
Honda
|
25
|
10
|
20
|
55
|
|
Total
|
60
|
50
|
50
|
160
|
A tourism management company is interested to investigate if there is any association between the Brand and Colour of the cars.
(a) In order to formally check if there is an association between the brand and colour of the cars, a hypothesis test is necessary. Write the relevant hypotheses in the context of this study.
(b) If there is no association between the brand and colour of the cars, how many cars would be expected in the Toyota brand and White colour cell/category?
(c) What is the contribution of the ‘Toyota brand and White colour' cell/category to the value of the test statistic?
(d) Using SPSS, find the observed value of the test statistic, and its degrees of freedom.
(e) Using an appropriate statistical table, find the P-value and write a contextual conclusion for the outcome of the test at the 1% level of significance.
(f) Quoting the value of the standardized residual from appropriate procedure in SPSS, comment on which colour and brand of cars are most under-represented.
Attachment:- Statistics for Quantitative Researchers.rar