. 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 = 60, and standard deviation of = 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 8^thgrade students when compared to the population?Conduct the six steps of hypothesis testing to find your answer and use = .01.