3. A student is able to swim the 25-yard butterfly with mean time of 16.43 seconds. He decides to try an adjustment to his stroke. For 15 random swims using the adjusted stroke, his mean time was 16.02 seconds with sample standard deviation 0.80 seconds. Test the claim that the adjustment helps him swim faster. In other words, test the claim the student's mean swim time for the 25-yard butterfly is less than 16.43 seconds when using the adjusted stroke. Use a 5% significance level. Assume swim times are normally distributed. a. Write the hypotheses. b. Identify sample statistics and given values symbollically. Include the degrees of freedom for the t-distribution. c. For this hypothesis test of a population mean, we will conduct a T-Test. Why do we conduct a T-Test rather than a Z-Test? d. What is the direction of the test? What word or words in the problem did you use to determine this? Answer in the form of a complete sentence. e. Find the CV on the t-table or using invT. Remember f. Find the TV using the T-Test. Round to 3 decimal choose the correct sign based on the direction of the test. places. Do NOT show a by-hand calculation. Graph the Graph the CV. Identify the CR. Shade alpha. TV. Shade the p-value. g. Write the p-value from your T-Test in decimal h. Traditional Method. i. P-value Method. form (4 dec places) and as a percent. Circle the correct statement: Circle the correct statement. TV is in the CR p-value a j. What is your decision? k. Circle the correct statement. At the significance level, there (is/is not) enough evidence to support the claim that the goggles Reject Ho Fail to reject Ho helped Marco swim faster. As well as the above, include the value of Ho on the graph. Make certain directional shading is clear (no "scribble" shading).