Solve the following:
Q1: A researcher is comparing the reaction times of a 10-year-olds who play video games and 10-year-olds who do not. 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 reaction time(Secs) 0.01 0.02
Assume that the reaction times for both populations are normally distributed with the same population standard deviation.
a. Construct a 98% confidence interval for the difference between the population means of reaction times.
Note: Express your answer to 5 decimal places of accuracy.
b. Using a 2.5% significance level, can the researcher conclude that the mean reaction time of players of video games is less than the mean reaction time of non-players of video games? Formulate and test the appropriate hypothesis. Use the Critical value approach.