QUESTION 1 A random sample of monthly internet usage bills from three different telecommunication providers were collected among the university students at College H. The result as follow ANOVA Internet Usage Sum of Squares df Mean Square F Sig. Between Groups 1613.771 Q R S 069 Within Groups P 12 238.773 Total 4479.042 14 a) What are the TWO (2) main assumptions for the model above? (2 marks) b) Compute the values of P, Q, R and S. (4 marks) c) Using p-value approach, is there any evidence to indicate the mean internet usage bills among the university students are different from the three telecommunication providers? Use a=0.05.QUESTION 2 Hashim Motors Son. Bhd. specializes in selling a secondhand car. Currently, the company has 12 used cars for sale. The owner of the company wants to investigate the relationship between the age of the car and the mileage of the car. The data were collected and analyzed using SPSS. The results as follow. Car's age (years) 6 4 2 2.5 3 4 3 5 5.5 4.5 4.5 3.5 Mileage (000 km) | 93 60 33 36 53 59 48 77 79 61 63 50 Model Summary Adjusted R Sid. Error of the Model R R Square Square Estimate 975 951 946 4.036 Coefficients" Standardized Unstandardized Coefficients ConMiclients Model std. Error Betz Sig (Constant 3.827 4.134 950 365 Age 13.987 1.002 975 13.971 .000 a) Prove that the correlation coefficient is 0.975. (4 marks) b) Interpret the value of the correlation coefficient in a). (1 mark) c) State the value of the coefficient of determination. Interpret its meaning. (2 marks) d) Based on the SPSS output, write the complete regression equation. (1 mark) e) Based on the regression equation in d), interpret the slope in the context of the problem. (1 mark) f) Predict the mileage of the car if the age of the used car is 4.3 years.(1 mark)QUESTION 4 The owner of rental houses claims that the average length of occupancy is 3.2 years. A random sample of 35 rental contracts were selected and analysed using SPSS. One-Sample Statistics N Mean Std. Deviation Std. Error Mean Length (years) 35 3.446 1.0551 a) Show that T is 0.1783. (2 marks) b) Construct a 95% confidence interval for the average length of occupancy of properties owned by the owner. (3 marks) c) Based on the confidence interval in b), is the owner's claim true? Give a reason to support your answer. (2 marks) QUESTION 5 Ten employees were selected at random, and the data on the number of customers per month were recorded before and after the selected employees attending the workshop. The data were collected and analyzed using SPSS. The results as follow. Paired Samples Test Paired Differences 95% Confidence Interval of Std. Std. Error the Difference Mean Deviation Mean Lower Upper df Pair 1 Before - After 2.70000 3.71334 1.17426 04364 5.35636 2.299 a) The manager decided to analyze the data using Paired Samples Test. Give a reason to support his decision to use this statistical analysis.(1 mark) b) Show the value of t-statistic using appropriate formula. (3 marks) c) Can the insurance manager conclude that the workshop has increased the number of customers? Use a=0.10. (4 marks)QUESTION 7 A researcher wants to investigate whether the education level is related to his or her place of residence. Hundred's people were selected randomly. The results are given as follow. Area * Education Level Crosstabulation Education Level Bachelor's SPM Diploma Degree Total Area Urban Count 22 10 18 50 Expected Count 25.0 8.0 17.0 50.0 Rural Count 28 16 50 Expected Count 25.0 80 A 50.0 Total Count 50 16 34 100 Expected Count 50.0 16.0 34.0 100.0 Chi-Square Tests Value di Pearson Chi-Square IN Likelihood Ratio 1.850 2 Linear-by-Linear Association 778 N of Valid Cases 100 a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 8.00. a) State a reason of choosing the Chi-Square Test of Independence for this study. (1 mark) b) Calculate the values of A and B. (5 marks) c) At the 5% significance level, test whether education level is associated to his or her place of residence. (4 marks)