**Title: Analyzing Paddle Boarding Times with and without Music at Big Bear Lake****Introduction:**Big Bear Lake, with its 22 miles of shoreline, is a prime location for paddle boarders. A study was conducted to determine whether listening to music affects the paddle boarding times across the lake. Nine paddle boarders were timed under two conditions: paddling while listening to music and paddling without music. The recorded times (in minutes) are as follows:- **Listened to Music:** 44, 48, 49, 50, 45, 49, 44, 47, 44- **No Music:** 52, 54, 60, 54, 52, 59, 54, 57, 59**Objective:**To assess whether there is a statistically significant difference in the paddle boarding times under the two conditions at the significance level \(\alpha = 0.10\).**Methodology:**- **Test Used:** \(t\)-test for the difference between two dependent population means- **Null Hypothesis (\(H_0\)):** \(\mu_d = 0\)- **Alternative Hypothesis (\(H_1\)):** \(\mu_d \neq 0\)**Statistical Analysis:**- **Test Statistic:** \(-3.600\) (rounded to 3 decimal places)- **P-value:** \(0.0035\) (rounded to 4 decimal places)- **Decision based on p-value:** Reject the null hypothesis since the p-value is less than \(\alpha = 0.10\).**Conclusion:**The results are statistically significant at \(\alpha = 0.10\). Thus, there is sufficient evidence to conclude that paddle boarding with music leads to significantly faster times compared to paddle boarding without music.**Interpretation of Results:**- **Type I Error Probability:** There is a 0.35% chance of making a Type I error.- **Meaning:** If the true mean paddle boarding times are the same, the observed difference (music leading to faster times) is due to random sampling error only in 0.35% of similar tests.The study provides evidence supporting the hypothesis that listening to music positively impacts paddle boarding speed at Big Bear Lake.

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