2.5 Using a 5% level of significance, test all the possible hypotheses, namely. i) does the mean length of home visits differ among different age groups of nurses (Ho : M =0 =0=0)? ii) does the type of patient affect the mean length of home visit (H : 8 = A = = A)? ii') is there any interaction between the nurse's age and type of patient ((H. : (26) = 02 Provide the null and alternative hypotheses, critical region (or rejection region), test statistic and conclusions. (18) 2.6 Investigate the regression diagnostics for your model and comment on whether the assumptions have been met or not. (8)[60] Question 2 In a study of length of time spent on individual home visits by public health nurses, data were reported on the length of home visits (in minutes) for a sample of 80 nurses. A record was made on each nurse's age and the type of illness of each patient visited and is summarized in Table 1 below. The researchers' objective was to investigate the following: does the mean lengths of home visits differ among the age groups of the nurses, does the type of patient affect the mean length of home visits and is there any interaction between nurse's age and type of patient? Capture the data on an excel spreadsheet. Note that the data must be in the following format: Column 1 represents the observed lengths of time, column 2 identifies the type of patient and column 3 contains the age group of the nurse. Import the data in R and answer the questions that follow. Present or attach the relevant R outputs used to answer your questions. Table 1: Length of Home visits in minutes by Public Health Nurses by Nurse's age group and Type of patient Factor B (Age group of nurse in years) (30 -39] (40 -49) (50 and over) Factor A (Type of patient) (20 - 29] 25 24 28 Cardiac 20 25 30 28 31 29 24 20 25 21 30 30 30 32 40 Cancer 45 29 42 45 30 31 38 50 35 30 42 45 36 30 40 80 32 41 C.V.A 31 30 35 45 En 40 30 40 40 35 40 40 20 35 45 Tuberculosis 20 23 24 21 25 24 30 28 20 28 30 20 30 27 10 31 23 (6) 2.1 Produce interaction plots of the data and comment. 2.2 Give the appropriate model and assumptions. Note: You must define the termsotations (10) used in the model using the given information. (10) 2.3 Perform a two-way analysis of variance (ANOVA) and provide the ANOVA table 2.4 Estimate the variance components using the ANOVA method and interpret the results. (8) 3