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(d) What type of error might we have made? Explain what the error means in the context of the application. O Fielding Error O Type II O Type I O Throwing Error 14 2 (e) Based on the results of this hypothesis test, would you expect a confidence interval for the average difference between the reading and writing scores to include 0? Explain your reasoning. O yes, because there is almost a 0%% chance that average reading and writing scores are the same O no, because most people will not earn an average score of 0 on either exam O no, because we rejected the idea that average reading and writing scores are equal yes, because the evidence was not strong enough to suggest that average reading and writing scores differ5.20 High School and Beyond, Part I: The National Center of Education Statistics conducted a survey of high school seniors, collecting test data on reading, writing, and several other subjects. Here we examine a simple random sample of 200 students from this survey. Side-by-side box plots of reading and writing scores as well as a histogram of the differences in scores are shown below. 80 60- IT scores 40 20- read write 40- 30- 20- 10- -20 -10 0 10 20 Differences in scores (read - write)(a) Are the reading and writing scores of each student independent of each other? O no, they are paired since each student has both a reading score and a writing score O yes, because reading and writing are two different activities yes, they are paired since each student has both a reading score and a writing score (b) Create hypotheses appropriate for the following research question: is there an evident difference in the average scores of students in the reading and writing exam? O Ho: Hdiff = 0 Ha: Hair = 0 O Ho: Hdiff = 0 14.2 Ha: Hair *0 O Ho: Hdiff = 0 Ha: Haiff > 0 (c) The average observed difference in scores is Thread . write = -0.545, and the standard deviation of the differences is 8.887 points. Do these data provide convincing evidence of a difference between the average scores on the two exams! The test statistic is: (please round to two decimal places) The p-value is: (please round to four decimal places) The conclusion of the test is: O Since p 2 a we accept the null hypothesis Since p 2 a we reject the null hypothesis and accept the alternative Since pra we fail to reject the null hypothesis Since pra we reject the null hypothesis and accept the alternative Since p 2 a we do not have enough evidence to reject the null hypothesis