Question

You believe that caffeine increases the enjoyment of morning statistics classes. You know that in the general population, all other students in statistics classes have an average enjoyment of statistics class of 56 (measured on a scale from 1-100). This population also has a variance of 121 and that it is normally distributed. To test your idea you take one lucky volunteer student, Bob Ross, and give him 3 cups of coffee before a statistics class. After the class Bob rates his enjoyment of the class as 32. For this experiment you decide that α = 0.03. Use this data to answer the following questions:

1. What are the characteristics of your comparison distribution? (3 points)

2. What is the cutoff (critical) Z-score for this experiment?
3. What is you sample Z-score?
4. Based on your findings, what is your decision regarding the null hypothesis? Explain or show why you made this decision.
5. What are the overall conclusions you can draw from this study?

Answer 1

Here average enjoyment of statistics class = = 56

standard deviation of  enjoyment of statistics class = s = sqrt(121) = 11

Here bob's enjoyment of the class = 32

significance value  α = 0.03

Here comparison distribution is normal where x ~ NORMAL (56, 11)

sample Z - score = (32 - 56)/11 = -2.182

P - value = P(Z < -2.182) = 0.0146

Here we reject the null hypothesis as p - value is less than 0.03.

Here we can conclude that the mean enjoyment of statistics class reduce after taking coffee.

Here we conclude that