An individual has been exercising at a local gym for about 10 years. He always begins with a 10- to 15-minute session on the treadmill at a speed of 3.7 mph. During a 12-day period in 2010, he recorded his heart rate before using the treadmill and after 5 minutes of use. The data are shown in Table 8.37 (image attached).The subject also recorded his heart rate at baseline and 5 minutes after starting the treadmill exercise (at a speed of 2.5 mph) in 2000. The data are shown in Table 8.38 (image attached).Implement a test to compare the baseline heart rate initially (2000) and after 10 years of experience (2010), and report a two-sided p value. **Change in Heart Rate Following Treadmill Use in 2010***Table 8.37 displays the heart rate changes from a baseline measurement to five minutes after treadmill use in 2010. Each row represents a day or session of data collection.*| Day | Baseline | 5 min | Change ||-----|----------|-------|--------|| 1 | 85 | 103 | 18 || 2 | 77 | 92 | 15 || 3 | 81 | 97 | 16 || 4 | 81 | 96 | 15 || 5 | 74.5 | 93 | 18.5 || 6 | 83.75 | 96 | 12.25 || 7 | 76.5 | 93 | 16.5 || 8 | 77.75 | 94 | 16.25 || 9 | 79.25 | 90 | 10.75 || 10 | 84.25 | 99 | 14.75 || 11 | 76.5 | 94 | 17.5 || 12 | 84.75 | 97 | 12.25 |- **Mean Baseline:** 80.1- **Mean after 5 min:** 95.3- **Mean Change:** 15.2- **Standard Deviation (sd):** - Baseline: 3.7 - 5 min: 3.5 - Change: 2.4 **Change in Heart Rate Following Treadmill Use in 2000***Table 8.38 illustrates heart rate data from a baseline measurement to five minutes after treadmill use in 2000.*| Day | Baseline | 5 min | Day | Baseline | 5 min ||-----|----------|-------|-----|----------|-------|| 1 | 84 | 87 | 6 | 86 | 92 || 2 | 87 | 92 | 7 | 88 |

Name: An individual has been exercising at a local gym for about 10 years. H
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: An individual has been exercising at a local gym for about 10 years. He always begins with a 10- to 15-minute session on the treadmill at a speed of 3.7 mph. During a 12-day period in 2010, he recorded his heart rate before using the treadmill and af

Given Information : An individual has been exercising at a local gym for about 10 years. He always begins with a 10- to 15-minute session on the treadmill at a speed of 3.7 mph. During a 12-day period in 2010, he recorded his heart rate before using the treadmill and after 5 minutes of use. The data are shown in Table 8.37 (image attached). The subject also recorded his heart rate at baseline and 5 minutes after starting the treadmill exercise (at a speed of 2.5 mph) in 2000. The data are shown in Table 8.38 (image attached). Question of the problem : Is there change in the baseline heart rate initially (2000) and after 10 years of experience (2010), . The provided sample means for baseline heart rate initially (2000) and after 10 years of experience (2010), are shown below: Also, the provided sample standard deviations are: and the sample sizes are n1=10 and n2=12. Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: \mu_1μ1 = \mu_2μ2 Ha: \mu_1μ1 ≠ \mu_2μ2 This corresponds to a two-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used. Rejection Region Based on the information provided, the significance level is \alpha = 0.05α=0.05, and the degrees of freedom are df = 20df=20. In fact, the degrees of freedom are computed as follows, assuming that the population variances are equal: Hence, it is found that the critical value for this two-tailed test is t_c = 2.086tc=2.086, for \alpha = 0.05α=0.05 and df = 20df=20. The rejection region for this two-tailed test is R = \{t: |t| > 2.086\}R={t:∣t∣>2.086}. Test Statistics Since it is assumed that the population variances are equal, the t-statistic is computed as follows: Decision about the null hypothesis Since it is observed that |t| = 4.831 > t_c = 2.086∣t∣=4.831>tc=2.086, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p-value is p = 0.0001p=0.0001, and since p = 0.0001 < 0.05p=0.0001<0.05, it is concluded that the null hypothesis is rejected. Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that there change in the baseline heart rate initially (2000) and after 10 years of experience (2010), at the 0.05 significance level.