8 To compare the average swimming times for two swimmers, each swimmer was asked to swim freestyle for a distance of 100 yards at randomly selected times. The swimmers were thoroughly rested between laps and did not race against each other, so that each sample of times was an independent random sample. The times for each of10 trials are shown for the two swimmers.Swimmer 1Swimmer 259.6159.7559.8059.4259.4959.4459.3359.6259.6459.7159.7559.4959.4959.6259.6359.8260.0059.6959.8559.50In USE SALTSuppose that swimmer 2 was last year's winner when the two swimmers raced. Does it appear that the average time for swimmer 2 is still faster than the average time for swimmer 1 in the 100-yard freestyle? (Use Swimmer 1 - Swimmer 2. Use a = 0.05.)State the null and alternative hypotheses.O Ho: (H, - l2) = 0 versus H: (M, - H2) < 0O Ho: (H1 - U2) < O versus H,: (ly - H2) > 0O Ho: (H, - l2) = 0 versus H: (M, - H2) > 0O Ho: (H, - u2) + 0 versus H: (H, - H2) = 0O Ho: (H, - 2) = 0 versus H: (M, - H2) = 0State the test statistic. (Round your answer to three decimal places.)t = 0.301Find the approximate p-value for the test.O p-value < 0.005O 0.005 < p-value < 0.01oO 0.010 < p-value < 0.025O 0.025 < p-value < 0.050O 0.050 < p-value < 0.100O p-value > 0.100Interpret the results.O H, is rejected. There is sufficient evidence to conclude that the average time for swimmer 2 is still faster than that of swimmer 1.O H, is not rejected. There is insufficient evidence to conclude that the average time for swimmer 2 is still faster than that of swimmer 1.H, is not rejected. There is sufficient evidence to conclude that the average time for swimmer 2 is still faster than that of swimmer 1.O H, is rejected. There is insufficient evidence to conclude that the average time for swimmer 2 is still faster than that of swimmer 1.

The random variable swimming time follows normal distribution. There are two independent samples which are Swimmer 1 and Swimmer 2. We have to test whether the average time for swimmer 2 is still faster than of swimmer 1 or not. This is two-independent sample t-test with right-tailed.The null and alternative hypotheses areEXCEL (Data Analysis) Procedure: Step 1: In EXCEL sheet, enter Swimmer 1 in one column and enter Swimmer 2 in one column. Step 2: In Data, select Data Analysis and choose t test: Two-Sample Assuming Unequal Variances. Step 3: In Input Variable 1 Range: select Swimmer 1. Step 4: In Input Variable 2 Range: select Swimmer 2. Step 5: Select Lables. Click Ok. EXCEL (Data Analysis) output:The value of the test statistic is t = 0.299. The appropriate p-value is p-value > 0.100. Interpretation: H0 is not rejected. There is insufficient evidence to conclude that the average time for swimmer 2 is still faster than of swimmer 1.