1. Is there a correlation between the results of the two scores? What is the magnitude and the type of the correlation? Provide a simple interpretation for the result. 2. Determine the simple linear regression equation. 3. What could be the score of the students in statistics if they got math aptitude scores of a. 807 b. 757 c. 937 Math Aptitude Elem. Statistics Student X Y 92 83 2 87 94 3 81 73 72 GB 5 65 72 Problem # 2 The table below shows the "first time' driving test results of a sample of 200 individuals classified by gender and success or failure in the examination. We wish to explore the association between the two variables Test the hypothesis on the relationship between gender and success/failure in driving test results. Gender and success or failure in first time driving test results Results of Driving Test GENDER SUCCESS FAILURE TOTAL Male 70 28Problem # 2 The table below shows the "first time' driving test results of a sample of 200 individuals classified by gender and success or failure in the examination. We wish to explore the association between the two variables Test the hypothesis on the relationship between gender and success/failure in driving test results. Gender and success or failure in first time driving test results Results of Driving Test GENDER SUCCESS FAILURE TOTAL Male 70 28 Female 50 52 TotalProblem # 3 Ten beauty queens were presented to two members of the board judges in a pre-pageant activity. The judges were asked to rate the overall rating of the beauty queens. Determine how close the association of the judges in their judgment Beauty Queens 2 3 5 6 7 8 9 10 Judge X 9.65 9.87 9.81 9.90 9.05 9.38 9.47 9.52 9.61 9.95 Judge Y 9.61 9.81 9.85 9.92 9.10 9.40 9.50 9.36 9.59 9.94 Problem # 4 (15 points) Is parental influence independent of the child's future career? A random sample of 350 students were surveyed and each students was asked to name the parent who influenced them in their future career. The data resulted from the survey is summarized in the following table: Business Engineering Education/Arts Total Mother 50 33 107 190 Father 35 65 60 160 Total 85 167 350 Question: Are parental influence and child's future career dependent at 5% level of significance? In other words, given the data collected above, is there a relationship between the parents and their child's future career that they have obtained?Problem # 5 Four brands of flashlight batteries are to be compared by testing each brand in five flashlights. Twenty flashlights are randomly selected and divided randomly into four groups of five flashlights each. Then each group of flashlights uses a different brand of battery. The lifetimes of the batteries, to the nearest days, are as follows. Brand A Brand B Brand C Brand D 4 10 3 8 12 9 7 8 10 8 12 9 8 7 9 5 Preliminary analyses indicate that the independent samples come from normal populations with equal standard deviations. At the 5% significance level, does there appear to be a difference in mean lifetime among the four brands of batteries?