A psychologist is interested in how the game "Words with Friends" affects the vocabulary skills of 8th graders in the United States. The psychologist conducts an experiment in which a random sample of n = 25 8th grade students are required to play "Words with Friends" for 1 hour per day for an entire week. At the end of the experiment, the students are given a standardized vocabulary test which has a mean of μ = 60, and standard deviation of σ = 10. The test is scored such that lower scores indicate a better vocabulary. The sample of 25 8th graders had a mean score of M = 55. [6pts total]
a. Is there a significant difference in average vocabulary score for the sample of 8th grade students when compared to the population? Conduct the six steps of hypothesis testing to find your answer and use α = .01.