Project 7 Math 102 Project 7 Round off answers to two decimal places. 50 Questions 1-19. Refer to the data below. Notice there are 50 people given with some being males and others being female. Next to each person is listed the highest level of education that the person completed. Determine if there is a significant relationship between the gender of the person and his/her education level. Use = 5% Find the Observed values from the data, the expected values, Null hypothesis, Alternate hypothesis, degrees of freedom, alpha, critical chi square, computed chi square and decision (Reject Ho or Fail to Reject Ho) (Refer to the answer sheet - Answers 1-19) Person # Gender Education 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Male Male Female Female Female Male Female Male Female Female Female Male Female Male Female Male Female Male Female Male Female Female Female Female Female 4 year 4 year 4 year 4 year 4 year 4 year 4 year 4 year 4 year 4 year 2 year 2 year 2 year 2 year 2 year 2 year 2 year 2 year 2 year 2 year 2 year 2 year 2 year 2 year 2 year Person # 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 Gender Education Female Male Female Female Male Female Female Female Male Female Female Male Male Female Female Female Male Female Female Female Male Male Female Male Female HS HS HS HS HS HS HS HS HS HS HS HS HS HS HS HS HS HS HS HS HS HS HS HS HS Page 1 of 5 Project 7 Math 102 20 - 26 . In an experiment designed to compare the effectiveness of different brands of pain relievers, a group of 320 individuals who complained of chronic pain were randomly assigned to three daily treatments: three tablets of Brand A, three tablets of Brand B or three placebos. After taking the treatments, each subject was questioned, to determine the effectiveness of their treatment. Their responses are classified in the table below. Based upon these sample results can one conclude that drug treatment and relief from pain are independent at a significance level of 1%. Find the expected values, Null hypothesis, Alternate hypothesis, degrees of freedom, alpha, critical chi square, computed chi square and decision (Reject Ho or Fail to Reject Ho) Even though you have to calculate Expected values you do not show them for this example 2, on the answer sheet. (Refer to answer sheet - Answers 20 -26) RESULTS Total Relief Some Relief No Relief Totals 27-32 27 28 29 30 31 32 BRAND A 25 27 47 99 BRAND B 31 36 58 125 PLACEBO 20 31 45 96 TOTALS 76 94 150 320 Matthew, a medical researcher, wants to determine if a positive linear relationship exists between the numbers of pounds a male is overweight and his blood pressure. He randomly selects a sample of 10 males and records the number of pounds that the individuals are over his \"ideal\" weight according to a medical weight chart and his systolic blood pressure. Mathew's sample data is listed in the table below. Find the correlation between number of pounds over ideal weight and blood pressure. Find the value of a in the formula y = a+bx Find the value of b in the formula y = a+bx Make a prediction for blood pressure(y) for the weight(x) given on the answer sheet. Find the value of coefficient of determination What percent of the variance in the blood pressure is accounted for by the variance in pounds over ideal weight? Page 2 of 5 Project 7 Math 102 Data Male Subject 1 2 3 4 5 6 7 8 9 10 33 - 38 33 34 35 36 37 38 Pounds Overweight(x) 12 8 20 17 14 23 6 4 15 19 Blood Pressure(y) 150 142 165 152 147 158 135 128 135 153 Craig, a marketing executive for a brewery company, wants to determine if there is a positive linear relationship between advertising expenditures and sales for their new lite beer product, Less Ale. He randomly samples 7 sales regions and records the sample data in the following table, where the x variable represents the advertising expenditure in thousands of dollars and the y variable represents the beer sales in million dollars. Find the correlation between advertising expenditures (x) and sales(y). Find the value of a in the formula y = a+bx Find the value of b in the formula y = a+bx Make a prediction for sales(y) for the advertising expenditures(x) given on the answer sheet. Find the value of coefficient of determination What percent of the variance in the sales is accounted for by the variance in advertising expenditures? Data Region # 1 2 3 4 5 6 7 Expenditure(x) 32 43 63 92 57 23 84 Sales(y) 38 35 42 50 40 35 41 Page 3 of 5 Project 7 39 - 44 39 40 41 42 43 44 Math 102 I.M.Smart, a statistics nerd, wants to investigate if there is a positive relationship between the number of hours a student studies for a statistics exam and the student's test grade. He randomly samples 12 students that are taking statistics at a community college and records the sample data in the following data. Find the correlation between advertising expenditures (x) and sales(y). Find the value of a in the formula y = a+bx Find the value of b in the formula y = a+bx Make a prediction for Test Grade(y) for the Studying Hours(x) given on the answer sheet. Find the value of coefficient of determination What percent of the variance in the Test Grades is accounted for by the variance in Studying Hours? Student # 1 2 3 4 5 6 7 8 9 10 11 12 Studying Hours 10 8 12 20 7 4 9 15 11 6 2 1 Test Grade 80 60 78 90 65 60 70 85 75 70 45 50 Page 4 of 5 Project 7 45-50 45 Math 102 Unrelated questions. Does the scatter diagram display a relationship between the two variables and if so, is it positive or negative a) positive 46 48 49 50 c) none Does the scatter diagram display a relationship between the two variables and if so, is it positive or negative a) positive 47 b) negative b) negative c) none If a scattergram displays data points that approach a line that rises as your eyes move left to right, the correlation will be closer to which value? a) +1 b) -1 c) 0 d) can not determine Which of the following correlations represents the least amount of relationship between two variables? a) -1 b) -.78 c) 0.15 d) 0.0 In Chi Square, if the conclusion is that the classifications are independent then the Calculated Pearson's chi- square test statistics is greater the Table critical chi square. a) True b) Sometimes true c) False d) Can not determine The shape of the chi square distribution is similar to the shape of the t-distribution. a) True b) Sometimes true c) False d) Can not determine Page 5 of 5