A past study on the reaction time of children with cerebral palsy reports a mean of 1.6 seconds on a particular task. A researcher believes that the mean reaction time can be reduced by using a motivating set of directions. A set of ten equivalent childrenis randomly selected and they complete the same task with the motivating set of directions. Assume the rection time is normally distributed. The reaction times for the ten children are recorded as follows: 1.4, 1.8, 1.1, 1.4, 1.3, 1.6, 0.9, 1.5, 1.9, and 1.2 seconds.

Required:
a. Test if there is sufficient evidence in the sample data to support the claim of the researcherat significance level of 0.01.
b. Set up the null and alternative hypothesis and construct an appropriate confidence interval to answer thehypothesis test question.