Q2: TOEFL test was given to students which is a standard test to measure the English language ability of non-native spea

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Q2: TOEFL test was given to students which is a standard test to
measure the English
language ability of non-native speakers. Students take one version
before the start of the
practice course of TOEFL test and another version after the
practice course ends. Before and
After scores for a possible random sample of 5 students are shown
in the table. The standard
deviation for the differences is 7.58. The average grades before
the practice were 33 and the
average grades after the practice was 51.

We are interested in determining whether taking the practice course
increases students’
grades, as measured by this test. And we want a test to see if
scores at the end of the
practice course are higher, on average, than scores before the
beginning of the course.
“Show all your work to receive full point”
(5 points)
a) Define the relevant parameter/s and state the hypothesis:



b) Find the statistics test:



c) Find the p-values:



d) Write your conclusion:




e) Compute and interpret a 99% confidence interval for the
improvement in average
TOEFL score test between the Before and After scores.