Answered: Assume that the two samples are…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal.

Refer to the accompanying data set. Use a

0.01

significance level to test the claim that women and men have the same mean diastolic blood pressure.

Women Men

70.0 69.0

94.0 65.0

81.0 67.0

67.0 60.0

71.0 65.0

80.0 69.0

57.0 59.0

50.0 40.0

71.0 67.0

88.0 65.0

67.0 83.0

59.0 73.0

73.0 53.0

63.0 77.0

67.0 53.0

89.0 91.0

57.0 79.0

84.0 79.0

69.0 61.0

63.0 73.0

69.0 80.0

71.0 101.0

88.0 59.0

71.0 78.0

65.0 71.0

69.0 84.0

70.0 65.0

83.0 67.0

73.0 57.0

91.0 83.0

62.0 78.0

71.0 56.0

77.0 62.0

91.0 67.0

85.0 71.0

59.0 48.0

78.0 64.0

81.0 76.0

77.0 73.0

85.0 53.0

75.0 67.0

60.0 61.0

63.0 67.0

77.0 77.0

60.0 73.0

68.0 74.0

65.0 65.0

53.0 89.0

66.0 65.0

73.0 75.0

65.0 48.0

73.0 88.0

79.0 89.0

66.0 69.0

85.0 72.0

60.0 66.0

93.0 73.0

57.0 87.0

77.0 55.0

73.0 92.0

59.0 83.0

78.0 88.0

65.0 94.0

91.0 87.0

46.0 89.0

46.0 101.0

67.0 71.0

70.0 83.0

56.0 70.0

71.0 65.0

66.0 64.0

71.0 70.0

70.0 71.0

65.0 54.0

74.0 75.0

64.0 65.0

72.0 79.0

56.0 91.0

57.0 80.0

79.0 87.0

71.0 65.0

70.0 71.0

63.0 77.0

66.0 77.0

83.0 59.0

53.0 67.0

76.0 83.0

73.0 71.0

51.0 67.0

91.0 68.0

57.0 71.0

83.0 75.0

81.0 71.0

77.0 67.0

66.0 77.0

73.0 67.0

63.0 50.0

88.0 65.0

55.0 72.0

76.0 67.0

77.0 77.0

91.0 52.0

64.0 54.0

69.0 66.0

80.0 85.0

42.0 85.0

74.0 72.0

71.0 81.0

46.0 70.0

72.0 55.0

88.0 85.0

78.0 83.0

69.0 59.0

67.0 69.0

71.0 65.0

81.0 67.0

65.0 71.0

99.0 63.0

67.0 65.0

71.0 78.0

61.0 86.0

69.0 77.0

68.0 95.0

75.0 96.0

59.0 75.0

69.0 80.0

53.0 73.0

55.0 56.0

69.0 77.0

69.0 74.0

75.0 50.0

76.0 76.0

40.0 82.0

73.0 67.0

57.0 81.0

69.0 75.0

79.0 83.0

65.0 54.0

73.0 84.0

65.0 98.0

67.0 67.0

55.0 68.0

96.0 68.0

71.0 69.0

65.0 46.0

83.0 57.0

53.0 51.0

67.0

44.0

82.0

63.0

74.0

70.0

**Hypothesis Testing for Mean Diastolic Blood Pressure**

Consider $\mu_1$ as the mean diastolic blood pressure for women and $\mu_2$ as the mean diastolic blood pressure for men. We need to determine the null and alternative hypotheses regarding these means.

**Options for Null and Alternative Hypotheses:**

- **A.**
- $H_0$: $\mu_1 = \mu_2$
- $H_1$: $\mu_1 > \mu_2$

- **B.**
- $H_0$: $\mu_1 < \mu_2$
- $H_1$: $\mu_1 = \mu_2$

- **C.**
- $H_0$: $\mu_1 \neq \mu_2$
- $H_1$: $\mu_1 = \mu_2$

- **D.**
- $H_0$: $\mu_1 = \mu_2$
- $H_1$: $\mu_1 \neq \mu_2$

**Statistical Analysis Steps:**

1. **Calculate the Test Statistic:**
- $ t = $ [box for input] (Round to two decimal places as needed.)

2. **Find the P-value:**
- P-value = [box for input] (Round to three decimal places as needed.)

3. **Make a Conclusion:**
- Conclusion regarding $H_0$: Select from a dropdown
- There [dropdown for input] sufficient evidence to warrant rejection of the claim that women and men have the same mean diastolic blood pressure.

**Note:** Fill in the calculations as needed on your study page.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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