Math 1111 Written Assignment 5 Relationships Between Variables

Math 1111 Written Assignment 5 Relationships Between Variables Instructions Please answer each of the following questions in order. There are two questions in total. You may write your answers neatly by hand or type them up, or a mix of the two. You will need to submit your assignment as a PDF file. You can use your phone to scan written work and convert to PDF. You may use any software or technology to answer the que stions below. You may also work by hand. I recommend (but do not require) that you use Microsoft Excel . Your assignment must be submitted on Moodle. Emailed submissions will not be accepted. Questions 1. Is there a relationship between gender and preferred ice cream flavour? A study surveyed 200 high school students and collected their scores on various tests, as well as their gender and preferred ice cream flavour out of three options given: chocolate, strawberry, and vanilla. The results are summarized in the table below. Chocolate Strawberry Vanilla Total Female 32 29 48 109 Male 15 29 47 91 Total 47 58 95 200 a. Create a table of sample proportions. It is recommended that you check that the table total equal s 100% . Chocolate Strawberry Vanilla Total Female Male Total 100 % b. What proportion of female students preferred chocolate ice cream? How does this compare to the proportion of male students who preferred chocolate ? c. Fill out the table of expected values for the chi -squared statistic. Retain 3 decimal places of accuracy. Chocolate Strawberry Vanilla Total Female 109 Male 91 47 58 95 200 d. What is the value of the chi -squared statistic ? Which factor (combination of gender and flavour) contributed the most to this sum? e. State the appropriate hypotheses for this chi -squared test. f. Find the appropriate degrees of freedom and calculate the p-value. At the = 0.05 level, do you find that there is evidence of a relationship? Give a conclusion that would make sense to a non -statistician. 2. For this question, use the cereal data set. a. Crea te a scatterplot of the data , plotting “ calories ” on the horizontal () axis and “ fibre ” on the vertical () axis . Make sure that you adhere to best practices for graphs: descriptive title, axis labels including units, and sensible axis scale. b. Comment on the strength and direction of this relationship . Calculate the correlation coefficient (you can use =CORREL in Excel). How does the value of this coefficient affirm what you said about the strength and direction of the relationship? c. Consider the data point at ( 120, 6 ). Without calculating the residual or the regression line, do you expect the residual for this dat a point to be positive or negative? Why? d. Calculate the equation of the regression line as follows. i. Find ? and ?. ii. Find and . iii. Find the slope using the equation = ( ). (You found in part (b).) iv. Find the intercept using the equation = ?? ?. v. State the equation in the form ?= + . e. Going back to the data point at ( 120, 6 ), find the value of the residual and confirm your answer to part (b). f. Use the regression equation to predict the fibre content of a cereal with 1 15 calories per serving.