A random 8 kindergarten children were recruited to participate pre and post instruction assessments. They were assessed before and after instruction and their grades were recorded to investigate whether there is a difference between pre and post grades:

ID	1	2	3	4	5	6	7	8
Pre	80	60	73	90	100	70	94	98
Post	85	63	77	92	100	85	96	100
Post-Pre

1. Construct a paired t test to investigate whether the difference between post and pre assessments is 0.

(show your work)

1. Write the null and alternative hypotheses
2. Calculate the point estimate (the average of grade difference)
3. Calculate standard error
4. Calculate the test statistics
5. Find the critical value
6. Find the p value
7. Interpret the result from t test statistics

2. Construct and interpret the 95% confidence interval to estimate the average grade difference between pre and post

(Show your steps to construct the 95% confidence interval)

3. make inference based on the test statistics in term of hypotheses