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A professor was interested in comparing how well her students performed on their midterm and final exams in her calculus course. She randomly sampled 7 students from her class and recorded their midterm and final exam grades which are shown in the table below.  Midterm and Final Exam Grade Comparisons Student X=Midterm Exam Y=Final Exam Student 1 75 76 Student 2 73 67 Student 3 87 93 Student 4 90 92 Student 5 72 66 Student 6 84 68 Student 7 91 88   Use this information to calculate the slope of the least squares regression line.  Make sure to type your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was 98.76543 then you would type in 98.765.

A researcher was interested in determining whether or not “Money can buy happiness”. He randomly sampled 300 individuals and asked them how much money they make annually as well as how happy they were at this point in their life on a scale from 1-10. He then proceeded to analyze the data and came up with the following regression equation where X represents the amount of money in tens of thousands of dollars that they made (i.e. $75,000 would correspond to 7.5) and Y represents their predicted happiness level:   Use this linear regression equation to predict the an individuals happiness level if their annual income is $40,000.  Type in your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was 6.54321 then you would type in 6.543. 

Suppose you have a jar that contains 10 marbles: 5 black, 3 yellow, and 2 orange. If you were to select 1 marble at random from the jar, return that marble to the jar and then select a second marble at random from the jar, what is the probability that both marbles would be black?   Type in your answer as a decimal rounded to 2 places. For example, if you thought the answer was 54.321% then you would type in 0.54. 

Consider the table below that shows how many students from each year are in each of the Hogwart’s houses. Use this information to answer the probability question that follows.  Hint: I would recommend finding the totals for each row and column first.  Probability Table Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Ravenclaw 30 38 34 33 39 31 35 Hufflepuff 36 33 29 37 39 35 34 Gryffindor 32 36 41 32 33 35 35 Slytherin 34 32 36 39 33 32 31   Find the probability that a randomly selected student is in Ravenclaw and Hufflepuff.   Make sure to type in your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was , then you would type in 0.431.

In 2019, a survey was conducted to try and determine whether or not MLS games drew in more fans than NBA games. The researchers randomly selected 40 games/matches from each sport and recorded the number of fans in attendance. In the 40 MLS games, there was an average of 20,870 fans per game with a sample standard deviation of 1,211 fans. In the 40 NBA games, there was an average of 18,212 fans with a sample standard deviation of 1,387 fans. Carry out the appropriate hypothesis test at the

Suppose you have a jar that contains 100 marbles: 35 red, 15 blue, 20 green, and 30 black. If you were to select 1 marble at random from the jar, what is the probability that you would select either a blue or green marble?   Type in your answer as a decimal rounded to 2 places. For example, if you thought the answer was 54.321% then you would type in 0.54. 

Suppose you were to flip a fair coin 12 times and you recorded the number of “Tails” that you received. Find the probability that you would get anywhere from 3 to 8 “Tails”. Make sure to type in your answer rounded to 2 decimal places. For example, if you thought the answer was 1.23456, then you would type in 1.23.

Suppose you roll a standard 6-sided die one time. What is the probability that you would roll a number less than 4? Recall that the sample space for this scenario would be .   Make sure to type in your answer as a decimal rounded to 2 decimal places. For example, if you thought the answer was 0.12345 then you would type in 0.12. 

Suppose you were to flip a fair coin 9 times and you recorded the number of “Tails” that you received. Find the probability that you would get exactly 5 “Tails” out of 9 coin tosses.  Make sure to type in your answer rounded to 2 decimal places. For example, if you thought the answer was 1.23456, then you would type in 1.23.

A professor was interested in comparing how well her students performed on their midterm and final exams in her calculus course. She randomly sampled 7 students from her class and recorded their midterm and final exam grades which are shown in the table below.  Midterm and Final Exam Grade Comparisons Student X=Midterm Exam Y=Final Exam Student 1 59 76 Student 2 65 67 Student 3 92 93 Student 4 80 92 Student 5 56 66 Student 6 50 68 Student 7 67 88   Use this information to calculate Pearson’s correlation coefficient.  Make sure to type your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was 0.54321 then you would type in 0.543.