In a game, a player throws a ball at a target. If they hit the target, then 7 points are
added to their score. If they miss the target, then 3 points are subtracted from their
score. A player’s score begins at 0, and it is possible for a player to have a negative
score.
(a) What is Shane’s score after 6 throws if 4 of the throws are hits and 2 of the
throws are misses?
(b) After exactly h hits and 6 misses, Susan’s score is 59. What is the value of h?
(c) After exactly 20 throws, Souresh’s score is greater than 85 and less than 105.
If exactly m of these throws are misses, determine all possible values of the
positive integer m.

A hexagonal prism has a height of 165 cm. Its two hexagonal faces are regular hexagons with sides of length 30 cm. Its other six faces are rectangles. A fly and an ant start at point X on the bottom face and travel to point Y on the top face. The fly flies directly along the shortest route through the prism. The ant crawls around the outside of the prism along a path of constant slope so that it winds around the prism exactly n + 1/2 times, for some positive integer n. The distance crawled by the ant is more than 20 times the distance flown by the fly.
What is the smallest possible value of n?

Problem 9 (15 points) Professor Dunderhead teaches statistics every semester exactly the same way. Scores on his final exams are remarkably consistent, with mean score 76.4 and standard deviation 7.3. This semester the professor discovers he has mistakenly been drinking decaffeinated coffee for years and switches to caffeinated coffee. He finds that a random sample of 15 of his students earns an average score of 79.7 on the final. He wonders if this is sufficient evidence to conclude his students this semester performed differently on the final than in years past. (b) Find the test statistic and p-value.

Problem 9 (15 points) Professor Dunderhead teaches statistics every semester exactly the same way. Scores on his final exams are remarkably consistent, with mean score 76.4 and standard deviation 7.3. This semester the professor discovers he has mistakenly been drinking decaffeinated coffee for years and switches to caffeinated coffee. He finds that a random sample of 15 of his students earns an average score of 79.7 on the final. He wonders if this is sufficient evidence to conclude his students this semester performed differently on the final than in years past. (a) Write down appropriate null and alternative hypotheses for this situation