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Answer :
- Compare the p-value to the significance level.
- Since $0.7429 > 0.07$, we fail to reject the null hypothesis.
- There is not enough evidence to support the claim that the ratio of the variances of Group A and Group B is less than some value $v$.
- Final Answer: \boxed{{\text{Fail to reject the null hypothesis}}}
### Explanation
1. Understand the problem and provided data
We are given two groups of data, Group A and Group B, and we want to perform a hypothesis test to see if the ratio of their variances is less than some value $v$. The null hypothesis is that the ratio of variances is approximately equal to $v$, and the alternative hypothesis is that the ratio is less than $v$. We are given a significance level of $\alpha = 0.07$. We are also given the sample means, sample standard deviations, and the F-statistic. The p-value is given as 0.7429.
2. Compare p-value to significance level
We are given the p-value as 0.7429. We need to compare this p-value to the significance level $\alpha = 0.07$.
3. Make a decision
Since the p-value (0.7429) is greater than the significance level (0.07), we fail to reject the null hypothesis.
4. State the conclusion
Therefore, we do not have enough evidence to support the claim that the ratio of the variances of Group A and Group B is less than some value $v$.
### Examples
In pharmaceutical research, comparing the variances of two drug formulations can help determine if one formulation has a more consistent effect than the other. If the variance of one formulation is significantly lower, it suggests that the drug's effects are more predictable. Hypothesis testing, like the one performed here, helps researchers make informed decisions about which formulations to pursue for further development and clinical trials.
- Since $0.7429 > 0.07$, we fail to reject the null hypothesis.
- There is not enough evidence to support the claim that the ratio of the variances of Group A and Group B is less than some value $v$.
- Final Answer: \boxed{{\text{Fail to reject the null hypothesis}}}
### Explanation
1. Understand the problem and provided data
We are given two groups of data, Group A and Group B, and we want to perform a hypothesis test to see if the ratio of their variances is less than some value $v$. The null hypothesis is that the ratio of variances is approximately equal to $v$, and the alternative hypothesis is that the ratio is less than $v$. We are given a significance level of $\alpha = 0.07$. We are also given the sample means, sample standard deviations, and the F-statistic. The p-value is given as 0.7429.
2. Compare p-value to significance level
We are given the p-value as 0.7429. We need to compare this p-value to the significance level $\alpha = 0.07$.
3. Make a decision
Since the p-value (0.7429) is greater than the significance level (0.07), we fail to reject the null hypothesis.
4. State the conclusion
Therefore, we do not have enough evidence to support the claim that the ratio of the variances of Group A and Group B is less than some value $v$.
### Examples
In pharmaceutical research, comparing the variances of two drug formulations can help determine if one formulation has a more consistent effect than the other. If the variance of one formulation is significantly lower, it suggests that the drug's effects are more predictable. Hypothesis testing, like the one performed here, helps researchers make informed decisions about which formulations to pursue for further development and clinical trials.
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