Listed below are systolic blood pressure measurements (mm Hg) taken from the right and left arms of the same woman. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Use a 0.01 significance level to test for a difference between the measurements from the two arms. What can be concluded? Right arm Left arm 148 179 In this example, "d is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the measurement from the right arm minus the measurement from the left arm. What are the null and alternative hypotheses for the hypothesis test? OA. Ho: Hd=0 H₁: Hd #0 130 136 143 138 179 183 153 139 OC. Ho: Hd #0 H₁: Hd = 0 OB. Ho: Hd=0 H₁: Hd <0 O D. Ho: Hd #0 H₁: Hd > 0

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**Blood Pressure Comparison Analysis**

Listed below are systolic blood pressure measurements (mm Hg) taken from the right and left arms of the same woman. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Use a 0.01 significance level to test for a difference between the measurements from the two arms. What can be concluded?

- **Right Arm**: 148, 136, 143, 138, 130
- **Left Arm**: 179, 179, 183, 153, 139

In this example, \( \mu_d \) is the mean value of the differences \( d \) for the population of all pairs of data, where each individual difference \( d \) is defined as the measurement from the right arm minus the measurement from the left arm. What are the null and alternative hypotheses for the hypothesis test?

**Options:**

- **A.** \( H_0: \mu_d = 0 \)  
         \( H_1: \mu_d \neq 0 \)

- **B.** \( H_0: \mu_d = 0 \)  
         \( H_1: \mu_d < 0 \)

- **C.** \( H_0: \mu_d \neq 0 \)  
         \( H_1: \mu_d = 0 \)

- **D.** \( H_0: \mu_d \neq 0 \)  
         \( H_1: \mu_d > 0 \)

**Explanation for the Educational Website:**

In this scenario, we are conducting a paired t-test to determine if there’s a significant difference between blood pressure readings between a woman's right and left arms. The null hypothesis (\( H_0 \)) posits that there is no difference (\( \mu_d = 0 \)), while the alternative hypothesis (\( H_1 \)) assesses whether a significant difference exists, potentially in a specific direction (e.g., right arm measurements being consistently lower than left arm ones).

This analysis requires considering the options given, specifically assessing which reflects the hypotheses that the researcher wants to test based on the given data and context.
Transcribed Image Text:**Blood Pressure Comparison Analysis** Listed below are systolic blood pressure measurements (mm Hg) taken from the right and left arms of the same woman. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Use a 0.01 significance level to test for a difference between the measurements from the two arms. What can be concluded? - **Right Arm**: 148, 136, 143, 138, 130 - **Left Arm**: 179, 179, 183, 153, 139 In this example, \( \mu_d \) is the mean value of the differences \( d \) for the population of all pairs of data, where each individual difference \( d \) is defined as the measurement from the right arm minus the measurement from the left arm. What are the null and alternative hypotheses for the hypothesis test? **Options:** - **A.** \( H_0: \mu_d = 0 \) \( H_1: \mu_d \neq 0 \) - **B.** \( H_0: \mu_d = 0 \) \( H_1: \mu_d < 0 \) - **C.** \( H_0: \mu_d \neq 0 \) \( H_1: \mu_d = 0 \) - **D.** \( H_0: \mu_d \neq 0 \) \( H_1: \mu_d > 0 \) **Explanation for the Educational Website:** In this scenario, we are conducting a paired t-test to determine if there’s a significant difference between blood pressure readings between a woman's right and left arms. The null hypothesis (\( H_0 \)) posits that there is no difference (\( \mu_d = 0 \)), while the alternative hypothesis (\( H_1 \)) assesses whether a significant difference exists, potentially in a specific direction (e.g., right arm measurements being consistently lower than left arm ones). This analysis requires considering the options given, specifically assessing which reflects the hypotheses that the researcher wants to test based on the given data and context.
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