A Psycholinguistic researcher is interested in investigating the effectiveness of his newly developed writing intervention program in reducing grammatical errors amongst undergraduate students. To assess the program's effectiveness, the researcher recruits a random sample of 8 undergraduate students and asks them to write a two-page essay. The researcher collects the essays and counts the number of grammatical errors (e.g., punctuation mistakes, subject-verb agreement errors, etc.) made by each participant. Next, the researcher administers a writing intervention program to the participants with a series of sessions where the participants complete practice exercises and receive feedback aimed at improving grammar skills. Upon completion of the writing intervention program, the researcher asks the same participants to write another two-page essay. The researcher collects the post-intervention program essays and again counts the number of grammatical errors made by each participant. Furthermore, the number of grammatical errors in the essays of the participants (identified by the researcher) comprises the data. The researcher is interested in determining whether or not there is a difference in grammatical errors made by participants before and after the intervention program. Assume a two-tailed, non-directional hypothesis test.

Use the data file(Participant #,Pre-Program,Post-Program 1,11,7 2,7,8 3,10,6 4,13,6 5,11,3 6,4,2 7,14,4 8,10,9)as needed to answer the following:

a. Do the data meet all the assumptions of the appropriate statistical test (i.e., assumption checks)? Why or why not? (To be eligible for full marks, please include screenshots of the relevant part of the jamovi output to support your answers) (1 mark)

b. Calculate the t-statistic by hand. Note, this involves a series of steps and calculations (e.g., one of those steps involves calculating sum of squares). Please show all your work and calculations for each step to be eligible for full marks. (4 marks)

Note: In Q1b) you are not being asked to determine statistical significance using the critical region/value approach. You are strictly being asked to conduct the appropriate calculation steps to compute the value of the t-test statistic by hand.

c. Conduct the appropriate t-test in jamovi and include a screenshot of the main analysis table from jamovi as your answer to this question. Verify that the t-statistic you calculated by handin1c) matches the value in the t-test table displayed in jamovi. (1 mark)

Note: your t-statistic value should be equal or very close (if you rounded values in your calculations) to the value reported in jamovi. For more precise calculations in line with jamovi, retain more decimal points in your calculations.

d.Make a decision about the null hypothesis using = .05. Why did you make this decision? (1 mark)