Advertisements for an instructional video claim that the techniques will improve the ability of Little League pitchers to throw strikes and that, after undergoing the training, players will be able to throw strikes on at least 60% of their pitches. To test this claim, we have 20 Little Leaguers throw 50 pitches each, and we record the number of strikes. After the players participate in the training program, we repeat the test. The table shows the number of strikes each player threw before and after the training. The data is in strikes1.csv or strikes1.xlsx.

1. 1) For the variables in your dataset calculate the difference between the number of strikes thrown before and after. (2 pts)

2. 2) Calculate the mean and standard deviation of the differences in strikes thrown. (4 pts)

3. 3) List the conditions that you must satisfy to perform an inference in this situation.

   Reference your text or notes if needed. Include indicating whether the data is paired or

   two independent samples (3 pts). For the project, assume the conditions are met.

4. 4) For this data set you will construct a 94% confidence interval.

   a. Determine the critical value that you will use (z* or t*n-1) ( 2 pts) b. If using a t-value for your critical value, determine the degrees of freedom that you must use, otherwise indicate N/A. (2 pts) c. Calculate the margin of error. (3 pts) d. Calculate the appropriate confidence interval. (2 pts) e. Interpret the results of your confidence interval. (2 pts)

5. 5) A coach reviewing this study wishes to know if there is a difference between the mean number of strikes thrown before and after the training. a. Based on the confidence level used above to construct your confidence interval, what is the appropriate significance level that you must use to perform a

   significance test. Explain how you determined this value. (1 pt) b. Write the null and alternative hypothesis to test this hypothesis. (2 pts) c. What type of test are your performing: Left tail, right tail or two tail? (2 pts) d. Compute the appropriate test statistic and p-value. Detail how you computed the p-value. (4 pts) e. Explain the decision and conclusion that should be made in this situation. (2 pts)

f. Is the result consistent with your interpretation of the confidence interval? Explain (2 pts)

data

Before	After
28	35
29	36
30	32
32	28
32	35
32	34
32	32
32	34
32	35
33	36
33	33
33	35
34	32
34	30
34	33
35	34
36	37
36	33
37	35
37	36