A researcher designed a study to test whether caffeine use enhanced performance time to run a 100 meter sprint. The participants (n=30) ran a 100 meter sprint before the consumption of caffeine on day 1 and then they ran another 100 meter sprint on the following day 2 after ingesting caffeine. The average time taken to run the 100 meter sprint on day 1 was (M₁) and the average to run on day 2 after caffeine was (M₂). The variance for this study was calculated to be (S²).Does caffeine use improve the running time in the 100 meter sprint (e.g., lower time)? Use all of the data provided to you below and test at an alpha of 0.05.

a)What is the null hypothesis?

b) what is the alternative hypothesis?

c) Maintaining the order of the means in the hypothesis you selected above, what is/are the critical value(s)?

d)Here are the values for your study: Rememberto maintain the order of the means used in the hypothesis you selected.

M₁= 20.34 M₂= 10.84 S²= 202.36 n=30

What is your obtained value?(numerical value only rounded to 2 decimal places)

e) Is it necessary for F-max to be calculated in this problem?

f)Given the results of the previous steps, is it necessary to calculate confidence intervals?

g)Are the results you obtained meaningful? Report the result here for your effect size, showing all your work and making an interpretation.