Researchers were interested in determining if grumpy old men were more likely to suffer heart disease than contented old men. A random sample of 300 men, aged between 55 and 65 years of age, was surveyed and their responses were recorded. Of the 100 grumpy old men surveyed 5 suffered from heart disease; of the 200 contented old men surveyed, 20 suffered from heart disease. Based on this information, which one of the following statements is FALSE?Group of answer choicesThe estimated difference in the incidence of heart disease for the two groups is -0.05.For constructing an approximate 95% confidence interval for (pgrumpy - pcontent ),the standard error is 0.0304.To test the hypothesis: Ho : pgrumpy - pcontent = 0 against a two-sided alternative, the standard error will necessarily be greater than the standard error used for constructing the corresponding confidence interval.If we doubled the sample size, but still observed that 5% of the old grumpy men suffered from heart disease and 10% of the contented old men suffered from heart disease, then we would conclude that, for this age group, grumpy old men are (significantly) less likely to suffer from heat disease than contented men of a similar age.From this sample we can conclude that grumpy men, aged 55 to 65 years old, are (significantly) less likely to suffer from heart disease than contented men of a similar age.
Question
Researchers were interested in determining if grumpy old men were more likely to suffer heart disease than contented old men. A random sample of 300 men, aged between 55 and 65 years of age, was surveyed and their responses were recorded. Of the 100 grumpy old men surveyed 5 suffered from heart disease; of the 200 contented old men surveyed, 20 suffered from heart disease. Based on this information, which one of the following statements is FALSE?Group of answer choicesThe estimated difference in the incidence of heart disease for the two groups is -0.05.For constructing an approximate 95% confidence interval for (pgrumpy - pcontent ),the standard error is 0.0304.To test the hypothesis: Ho : pgrumpy - pcontent = 0 against a two-sided alternative, the standard error will necessarily be greater than the standard error used for constructing the corresponding confidence interval.If we doubled the sample size, but still observed that 5% of the old grumpy men suffered from heart disease and 10% of the contented old men suffered from heart disease, then we would conclude that, for this age group, grumpy old men are (significantly) less likely to suffer from heat disease than contented men of a similar age.From this sample we can conclude that grumpy men, aged 55 to 65 years old, are (significantly) less likely to suffer from heart disease than contented men of a similar age.
Solution
The statement that is FALSE is: "From this sample we can conclude that grumpy men, aged 55 to 65 years old, are (significantly) less likely to suffer from heart disease than contented men of a similar age."
This is because the data only provides a snapshot of the incidence of heart disease in these two groups at one point in time. It does not provide evidence of a causal relationship between being grumpy and having a lower risk of heart disease. To establish such a relationship, a more comprehensive study would need to be conducted, possibly involving tracking the health outcomes of a group of men over time and controlling for other factors that could influence heart disease risk.
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