To study the association between the diabetic patients and their family history of diabetes, the following data were obtained on 70 subjects.  

Which test is appropriate in this situation? Check whether the diabetes runs with generations in families or not at 5% level of significance using appropriate test.  

A random sample of 440 patients of cardiology department of a hospital was taken and their workout timing and severity of heart disease status were recorded. The following table shows the workout timing and severity of heart disease:  

 Test at 5% level of significance whether workout habit and heart disease are associated with to each other or not.  

A popular café chain wishes to improve customer service and its employee scheduling based on the daily customers’ footfall during past 10 weeks. The numbers of customers served in the restaurants during that period are given as follow: 

 i) Determine the seasonal indices for these data using a 7-day moving averages.
ii) Obtain the deseasonalised values.
iii) Fit the appropriate trend for the deseasonalised data using the least-squares method by matrix approach that best describes these data.
iv) Project the number of customers on Wednesday of the 22th week.
v) Plot the original data, the deseasonalised data, and the trend. 

A researcher is interested in studying the impact of the weekly working hours and type of machine used (0 for Machine A and 1 for Machine B) on the number of produced items of a particular type. The data were collected for 40 weeks and shown in the following table:

 i) Prepare a scatter plot to get an idea about the relationship among the variables.
ii) Fit a linear regression model and its related analysis at 1% level of significance.
iii) Does the fitted regression model satisfy the linearity and normality assumptions?
iv) Also, draw both fitted regression lines on the scatter plot. 

A company designs decorative glass wall panels. Each panel is supposed to meet company standards for such things as glass thickness, ability to reflect, size of panel, quality of glass, colour, and so on. To control these features, the company quality people randomly sampled the panels from every shift and determined how many of the panels are out of compliance on at least one feature. The data collected from 25 such samples are shown below:  

 Construct a suitable control chart for fraction of out of compliance panels to check whether the process is said to be in a state of control or not using both approaches. Also construct the revised control charts, if necessary.

A manager of an amusement park wanted to study the waiting times of visitors for issuing entry tickets during a peak hour. A subgroup of 15 visitors was selected (one at each ten minutes interval during an hour) and the time (in minutes) was measured from the point each visitor entered in the line to when he or she began to be attended. The results of 40 days period are recorded in the following table:

 The manager of this amusement park needs to construct suitable control charts for variability as well as average to infer whether the waiting times of visitors for getting entry tickets is under statistical control or not. If it is out-of-control, she also computes the revised control limits, if necessary.  

An investigation was performed to study the impacts of different types of machines on the production of a particular variety of toys. The six machines (A, B, C, D, E and F) are assigned at random to 36 cells of the square with the restriction that each machine is used only once by each operator and in each time-period. The following design was obtained in which 6 operators are arranged in “columns" and 6 time-periods are in “rows": 

 The average production in a day is given as follows:  

 Assuming that the effect of each operator, time-period and machine are normally distributed with approximately equal variances, analyse the design at 1% level of significance. Test whether the effect of the different operators, time periods and machines on the production are significant or not. If significant, do the pair-wise comparison between them.  

An experiment was conducted to compare two metals: A and B, as bonding agents for an alloy material. Components of the alloy were bonded using the metals as bonding agents, and the pressures required to break the bonds were measured. The data for the pressures required for breaking the metal are given in the following table:

 If the pressure required to break both metals are normally distributed, then answers the following questions:
i) Are the variances of the distributions of the pressure of Metals A and B equal at 5% level of significance?
ii) If yes, check whether the average pressure for Metal A is more than the Metal B at 5% level of significance? 

The scores (out of 100) secured by 60 employees of three different departments D1, D2 and D3 who participated in a study, are presented in the following table:

 i) Compute the correlation coefficient between scores of the employees working in department D1 and the joint effects of scores of the employees of departments D1 and D2.

ii) Compute the correlation coefficient between scores of the employees working in departments D1 and D2 after eliminating the linear effect of the scores of departments D3.

iii) Also represent the scores obtained by departments D1, D2 and D3 using box plot. 

A cooking oil supplier distributed two types of oils, say Oil A and Oil B to a large numbers of retail stores. The supplier wants to compare the popularity of both oils. For this purpose, he selects a sample of 100 stores and tracks record of the sold oils (in litres) of each type at each store. The data are noted in the following table:  

 Answer the following:
i) Which type of oil has more average sales?
ii) Which oil shows greater variability in the sales?
iii) Determine the correlation between both types of oils.
iv) Compute suitable width of the class intervals for both oils,
v) Construct the continuous frequency distribution for both oils. 

A study was conducted on 185 patients aged more than 45 years which are followed until the time of death or up to 10 years, whichever comes first. The patients have different covariates: age, gender (male/female), systolic blood pressure, smoking (yes/no), total serum cholesterol and diabetes (yes/no). The objective of this study is to determine which covariate influences the survival time. An analysis is conducted to investigate differences in all-cause mortality between men and women participating in the study. Suppose we obtain the following results after applying the Cox regression hazard model analyses:

 (i) Obtain hazard ratio and interpret the results.
(ii) Find the 99% confidence interval for the hazard ratio.
(iii) Test whether the covariates are significant or not at 1% level of significance. 

Describe censoring and differentiate between different types of censoring with the help of examples which are not considered in Block 4 of MSTE-004.  

The following data on diagnosis of coronary heart disease (where 0 indicating absence and 1 indicating presence), serum cholesterol (in mg/dl), resting blood pressure (in mmHg) and weight (in kg) were obtained for 80 patients to explore the relationship of coronary heart disease with cholesterol and weight. 

 (i) Fit a multiple logistic model for the dependence of coronary heart disease on the average serum cholesterol and weight considering  and   as the initial values of the parameters (solve only for one Iteration). (ii) Test the significance of the fitted model using Hosmer-Lemeshow test at 5% level of significance.  

Kaplan and Meier method

Poisson regression  

Polytomous logistic models

Suppose a researcher wants to evaluate the effect of cholesterol on the blood pressure. The following data on serum cholesterol (in mg/dL) and systolic blood pressure (in mm/Hg) were obtained for 15 patients to explore the relationship between cholesterol and blood pressure: 

 (i) Fit a linear regression model using the method of least squares.
(ii) Construct the normal probability plot for the data on serum cholesterol and systolic blood pressure.
(iii) Test the significance of the fitted regression model. 

Explain the assumptions underlying multiple linear regression model. 

A random sample of 250 patients was selected and their workout timing and diabetes status were recorded. The following table shows the workout timing and severity of diabetes: 

Test at 5% level of significance whether workout habit and diabetes are associated with to each other or not. 

Differentiate between Chi-square tests for association and homogeneity of proportions. Also mention the assumptions of these tests.