Big Bear lake has 22 miles of shoreline and is an ideal place for paddle boarders. A researcher wants to know if the time it takes to paddle board across Big Bear Lake decrease when the paddle boarder listens to music? Nine paddle boarders were timed as they paddle boarded across Big Bear Lake while listening to music and again while not listening to music. The resulting times, in minutes, are shown in the table below. Paddle Boarding Time to Cross Big Bear Lake Listened to Music 44 38 49 50 40 45 45 41 54 No 47 44 52 5o 42 53 44 47 59 Music Assume a Normal distribution. What can be concluded at the the a = 0.10 level of significance? For this study, we should use t-test for the difference between two dependent population means a. The null and altemative hypotheses would be: Họ: pd H: pd b. The test statistic t v = -3.600 (please round your answer to 3 decimal places.) c. The p-value = 0.0035 d. The p-value is 3 Va e. Based on this, we should (reject f. Thus, the final conclusion is that ... O The results are statistically insignificant at a = 0.10, so there is insufficient evidence to conclude that the population mean paddle boarding time with music is less than the population mean paddle boarding time without music. (Please round your answer to 4 decimal places.) ]the null hypothesis. O The results are statistically significant at a = 0.10, so there is sufficient evidence to conclude that the nine paddle boarder finished in less time on average with music compared to paddle boarding without music. The results are statistically significant at a = 0.10, so there is sufficient evidence to conclude that the population mean paddle boarding time with music is less than the population mean paddle boarding time without music. O The results are statistically insignificant at a = 0.10, so there is statistically significant evidence to conclude that the population mean paddle boarding time with music is equal to the population mean paddle boarding time without music. g. Interpret the p-value in the context of the study. O lf the sample mean paddle boarding time with music for the 9 paddle boarders is the same as the sample mean paddle boarding time without music for these 9 paddle boarders and if another 9 paddle boarders are observed paddle boarding the 10K with and without music then there would be a 0.35% chance of concluding that the mean paddle boarding time with music for the 9 paddle boarders is at least 3.6 minutes less than the mean paddle boarding time for these 9 paddle boarders without music. O There is a 0.35% chance of a Type I error. O There is a 0.35% chance that the mean paddle boarding time for the 9 paddle boarders with music is at least 3.6 minutes less than the mean time for these 9 paddle boarders without music. O lf the population mean paddle boarding time with music is the same as the population mean paddle boarding time without music and if another 9 paddle boarders compete with and without music then there would be a 0.35% chance that the mean paddle boarding time for the 9 paddle boarders would be at least 3.6 minutes less with music compared to them paddle