Recovery times for a disease for 3 types of drugs are tested on 3 groups of people with the following resultsd1 = [13, 10, 11, 10, 13, 10, 12, 10, 11, 10, 13, 11, 12, 9, 12]d2 = [10, 8, 10, 10, 9, 9, 7, 12, 14, 12, 12, 14, 14, 11, 13]d3 = [11, 10, 9, 8, 13, 9, 7, 11, 10, 9, 12, 8, 14, 11, 14]Test the hypothesis that the mean recovery time is the same, at a significance level of 0.05.
Question
Recovery times for a disease for 3 types of drugs are tested on 3 groups of people with the following resultsd1 = [13, 10, 11, 10, 13, 10, 12, 10, 11, 10, 13, 11, 12, 9, 12]d2 = [10, 8, 10, 10, 9, 9, 7, 12, 14, 12, 12, 14, 14, 11, 13]d3 = [11, 10, 9, 8, 13, 9, 7, 11, 10, 9, 12, 8, 14, 11, 14]Test the hypothesis that the mean recovery time is the same, at a significance level of 0.05.
Solution
To test the hypothesis that the mean recovery time is the same for the three types of drugs, we can use the Analysis of Variance (ANOVA) test. The ANOVA test is used to compare the means of more than two groups.
Here are the steps to perform the ANOVA test:
- Import the necessary libraries:
import scipy.stats as stats
- Define the data:
d1 = [13, 10, 11, 10, 13, 10, 12, 10, 11, 10, 13, 11, 12, 9, 12]
d2 = [10, 8, 10, 10, 9, 9, 7, 12, 14, 12, 12, 14, 14, 11, 13]
d3 = [11, 10, 9, 8, 13, 9, 7, 11, 10, 9, 12, 8, 14, 11, 14]
- Perform the ANOVA test:
F, p = stats.f_oneway(d1, d2, d3)
- Print the results:
print('F statistic:', F)
print('p-value:', p)
- Interpret the results: If the p-value is less than the significance level (0.05), we reject the null hypothesis that the means are equal. If the p-value is greater than the significance level, we fail to reject the null hypothesis.
Please note that this is a simplified explanation and the actual interpretation of the results may require a deeper understanding of the subject matter and additional context.
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