Statistical Analysis
MA 222 – Statistical Analysis Problem Set #2 NAME: TOTAL: 80 PTS SCORE:_______ Angelique Silvestri Before you start working on this problem set, please make sure to read the instructions posted thoroughly. If something is not clear, let me know right away. ALL work must be shown/explained to receive credit. Pay attention to the grading rubric so you will understand how you will be graded. QUESTION #1 (10 PTS) a. Provide an example of two quantitative variables that are positively associated/correlated. Indicate which one is your x-variable and your y-variable. Explain your reasoning as to why you think they are positively associated. Write your final answer below: b. Provide an example of two quantitative variables that are negatively associated/correlated. Indicate which one is your x-variable and your y-variable. Explain your reasoning as to why you think they are negatively associated. Write your final answer below: QUESTION #2 (40 PTS) The following table shows data on average per capita wine consumption and heart disease rate in a random sample of 10 countries. Yearly wine consumption 2.5 in liters (x) 3.9 2.9 2.4 2.9 0.8 9.1 2.7 0.8 0.7 Death from diseases (y) 167 131 191 220 297 71 172 211 300 heart 221 a. Create a scatter plot of the data. (5 PTS) Insert/Paste the scatter plot below: b. Use EXCEL’s regression function to find the equation of the least-squares regression line. (5 PTS) Write your answer below: c. Explain in words what the slope and y-intercept of the regression line tells us. (5 PTS) Write your answer below: d. By calculating the regression coefficient ( r ), how well does the regression line fit the data? Explain your response. (5 PTS) Write your answer below: e. Do the data provide convincing evidence that there is a linear relationship between the amount of alcohol consumed and the heart disease death rate? Carry out an appropriate hypothesis test (provide the initial and alternative hypotheses completely), calculate the p-value, and use a significance level of 0.05 for this question. (15 PTS) Write your answer below: f. If the average per capita wine consumption of a certain country is 5 liters, predict the number of deaths from heart diseases. Round your answer to the nearest whole number. (5 PTS) g. By calculating the coefficient of determination (r2), how many percent of the variation in the deaths from heart diseases can be explained by variation in the average per capita of wine consumption, using the regression line? How many percent is predicted by other factors? (5 PTS) Write your answer below: h. Other than the average wine consumption, can you give 3 factors that you think (meaning, your opinion) could affect the number of deaths from heart diseases? (5 PTS) Write your answer below: QUESTION #3 Refer to your z- table to answer the following questions. You must shade the part of the graph in question and write your final answer in percent form. a. What is the percentage of data below z = 1.35? (5 PTS) Graph: Final Answer: b. What is the percentage of data above z = -0.75? (5 PTS) Graph: Final Answer: c. What is the percentage of data between z = -1.23 and z = 1.45? (5 PTS) Graph: Final Answer: QUESTION #4 Refer to your z-table and answer the following questions and shade the area/interval that is being asked. a. For which value of z will you find the lowest 75% of the data? (5 PTS) ________________________ b. For which interval of z will you find the lowest 35% of the data? (5 PTS) ________________________ c. For which value of z will you find the lowest 5% of the data and the upper 5% data? (10 PTS) Lower 5% = ________________________ Upper 5% = ________________________
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