Question 1: Recently, a group of English teachers have thought up a new curriculum that they think will help with essay writing in highs schools. Though, while they think it will be a good idea, they would like to examine the way of teaching statistically so that they can be sure. They take a class of 60 students and teach them using this new method. They then take grades they get in their end of year essay assignment and find that their average scores were 74. Further, they look up the national average grade and the standard deviation for this class, which is also given below. The maximum score one can get in this assignment is 100 [25 pts]

The national average is 70 points with a standard deviation around this of 15 points.

Did this new curriculum have a significant impact on grades? Assume an alpha level of .05 Note: Please make show all of the steps we covered when formally testing hypotheses!

Question 2: A popular radio show recently suggested that spending 10 minutes a day doing mental math makes people happier (shocking right?!?). Being the young scholars that you are, you wish to test if this is true. You gather a group of eight people (N = 8) and measure their average happiness. Then you have them spend 10 minutes doing mental math everyday for a week and then measure their average happiness again. Did doing mental math make people significantly happier? Assume an alpha level of .05 [35 pts]

Happiness Scores:

Before Mental Math: 9, 13, 15, 17, 11, 14, 8, 13 After Mental Math: 13, 19, 21, 22, 13, 17, 15, 12

Note: Please make show all of the steps we covered when formally testing hypotheses!

Question 3: A popular radio show recently suggested that when commuting on a bicycle, people tend to eat more doughnuts. To test this, you found a group of 8 people who would be willing to ride a bike to work for the next month. You first figure out how many doughnuts per week they ate on a normal basis, then you have them commute to work on a bike for a whole month! During the last week of their biking, you again measure how many doughnuts they eat (the data is provided below). Determine if there is any truth to the claims made in the radio show. Assume an alpha level of .05.

Doughnuts Eaten:

Before Bike Commuting: 2, 3, 6, 7, 4, 8, 6, 4 After Bike Commuting: 4, 5, 7, 8, 10, 8, 8, 6

Note: Please make show all of the steps we covered when formally testing hypotheses!

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