It describes heart rate variability in patients before and after a certain treatment. Your task is to decide whether this treatment was successful. Run t-test for dependent samples. IMPORTANT:
It describes heart rate variability in patients before and after a certain treatment.
Your task is to decide whether this treatment was successful. Run t-test for dependent samples.
IMPORTANT:
In your response,
- write the null hypothesis and alternative hypothesis;
- your chosen a-level;
- p-level for calculated t-test;
- your decision on whether you reject the null hypothesis.
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Heart-rate variability before treatment |
Heart-rate variability after treatment |
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1402.73189164561 |
2076.68628032823 |
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2630.82323539157 |
343.393243579664 |
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17.9925778973231 |
461.716923403535 |
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15.3476564624503 |
815.003645304419 |
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111.18027545386 |
453.188649152339 |
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1434.48327919346 |
848.938707440178 |
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196.60024361565 |
5099.81860382564 |
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1950.47014166244 |
475.291619246818 |
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114.072124382794 |
848.938707440178 |
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497.014081405137 |
640.165841666279 |
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1395.20722739437 |
1719.49780325398 |
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3804.92519926187 |
1780.77378633543 |
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1395.20722739437 |
848.938707440178 |
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538.466206858172 |
556.805942961282 |
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369.719247193389 |
801.692366877669 |
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61.0189789653785 |
467.385367740218 |
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1253.19982622539 |
174.217051245943 |
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241.504116287217 |
65.3973170895067 |
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73.589155096492 |
17.0495447379701 |
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456.227041813414 |
11.2479068117749 |
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93.0238538715493 |
17.0495447379701 |
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5516.32204262122 |
275.656180594758 |
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654.091618987773 |
179.416186614151 |
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State the null and alternative hypotheses:
The investigator is specifically interested to test whether the treatment was successful or not.
Here, d = Before – After.
Denote µd as the population mean difference in the heart rate variability in patients before and after a certain treatment.
The null and alternate hypotheses are stated below:
Null hypothesis H0:
H0 : µd = 0
That is, there is no significant difference in the heart rate variability in patients before and after a certain treatment.
Alternative hypothesis H1:
H1 : µd ≠ 0
That is, there is a significant difference in the heart rate variability in patients before and after a certain treatment.
In order to test the hypothesis regarding the significant difference between a paired set of n observations (xi, yi), a paired t-test is appropriate.
Thus, the sampling distribution used in the given scenario is “Student’s t” by assuming that d has an approximately normal distribution.
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