1. A professor measured the time (in seconds) required to catch a falling meter stick for 19 randomly selected students' dominant and non-dominant hand. The professor claims that the reaction time in an individual's dominant hand is less than the reaction time in their non-dominant hand. At the 0.05 significance level, test the claim that the reaction time in an individual's dominant hand is less than the reaction time in their non-dominant hand. (The results can be found in the first two columns of the Excel file).

a. If we conduct statistical inference for this problem, what is (are) the parameter(s) we are conducting inference on? (You may state your answer in words or symbols).

b. Depending on your answer to part (a), construct one or two probability plots and one or two boxplots to visualize the distribution(s) of your sample data. If you construct two probability plots and two boxplots, please construct two separate Minitab probability plots and one Minitab boxplot displaying both boxes on the same graph. Copy and paste these graphs into your assignment. Below the graphs, answer the following questions.

i. Are there any major deviations from normality?

ii. Are there any outliers present?

iii. Is it appropriate to conduct statistical inference procedures, why or why not?

c. At the 0.05 significance level, test the claim that the reaction time in an individual's dominant hand is less than the reaction time in their non-dominant hand.

i. State the null and alternative hypotheses.

ii. State the significance level for this problem.

iii. Calculate the test statistic.

iv. Calculate the P-value and include the probability notation statement.

v. State whether you reject or do not reject the null hypothesis.

vi. State your conclusion in context of the problem (i.e. interpret your results).

d. Construct a 97.5% confidence interval for the above data. Interpret the confidence interval as we learned in class.