A researcher is comparing reaction times of Ten year-olds who play video games and 10-year-olds who don't. Random samples from each group provided the following results below:

Reaction time of 10-year-olds

Players of Video games Non-players of Video games

Sample Size 15 10

Mean reaction time (Seconds) 0.50 0.52

Standard deviation of the reaction time(Secs) 0.01 0.02

Suppose that the reaction times for both populations are normally distributed with the same population standard deviation.

a. Construct a 98% confidence interval for difference between the population means of reaction times.

Note: Express your answer to 5 decimal places of accuracy.

b. Using 2.5% significance level, can the researcher conclude that mean reaction time of players of video games is less than the mean reaction time of non-players of video games? Make and test the appropriate hypothesis. Employ the Critical value approach.

Please show work