Reduced heart rate variability (HRV) is known to be a predictor of mortality after a heart attack. One measure of HRV is the average of normal-to-normal beat interval (in milliseconds) for a 24-hour time period. Twenty-two heart attack patients who were dog owners and 80 heart attack patients who did not own a dog participated in a study of the effect of pet ownership on HRV, resulting in the summary statistics shown in the accompanying table. Measure ofHRV (averagenormal-to-normalbeat interval) MeanStandardDeviationOwns Dog874136Does Not Own Dog801133(a) The authors of this paper used a two-sample t test to test H0: ?1 - ?2 = 0 versus Ha: ?1 - ?2 ≠ 0. What assumptions must be reasonable in order for this to be an appropriate method of analysis?We must assume that the population distributions ---Select--- are aren't approximately normal.(b) The paper indicates that the null hypothesis from Part (a) was rejected and reports that the P-value is less than .05. Carry out the two-sample t test. Is your conclusion consistent with that of the paper?YesNo

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Description: Reduced heart rate variability (HRV) is known to be a predictor of mortality after a heart attack. One measure of HRV is the average of normal-to-normal beat interval (in milliseconds) for a 24-hour time period. Twenty-two heart attack patients who w

(a) For the two-sample t test to be an appropriate method of analysis it must be assumed that the two population distributions are approximately normal. Thus, we must assume that population distributions are approximately normal.(b) Assume that the variances of two populations are equal. The pooled variance is, sp2=n1-1s12+n2-1s22n1+n2-2=22-11362+80-1133222+80-2=17858.47 The pooled variance is 17858.47. The test statistic is, t=x¯1-x¯2sp21n1+1n2=874-80117858.47122+180=7332.1711=2.2691 The test statistic is 2.2691. The degrees of freedom is, df=n1+n2-2=22+80-2=100 The degrees of freedom is 100. The hypothesis is two tailed. The probability of t not equal to 2.2691 with 100 degrees of freedom can be obtained using the excel formula “=T.DIST.2T(2.2691,100)”. The probability value is 0.0254. Decision rule: If P-value≤α, then reject the null hypothesis. Otherwise, do not reject the null hypothesis. Conclusion: The P-value (0.0254) is greater than the level of significance (0.05). Based on decision rule, reject the null hypothesis. Yes, the conclusion is consistent with that of the paper.

Answered: (a) The authors of this paper used a…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Reduced heart rate variability (HRV) is known to be a predictor of mortality after a heart attack. One measure of HRV is the average of normal-to-normal beat interval (in milliseconds) for a 24-hour time period. Twenty-two heart attack patients who were dog owners and 80 heart attack patients who did not own a dog participated in a study of the effect of pet ownership on HRV, resulting in the summary statistics shown in the accompanying table.

Measure of
HRV (average
normal-to-normal
beat interval)

	Mean	Standard Deviation
Owns Dog	874	136
Does Not Own Dog	801	133

(a) The authors of this paper used a two-sample t test to test H₀: ?₁ - ?₂ = 0 versus H_a: ?₁ - ?₂ ≠ 0. What assumptions must be reasonable in order for this to be an appropriate method of analysis?
We must assume that the population distributions ---Select--- are aren't approximately normal.

(b) The paper indicates that the null hypothesis from Part (a) was rejected and reports that the P-value is less than .05. Carry out the two-sample t test. Is your conclusion consistent with that of the paper?

YesNo

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