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Answer :
To address the question of whether Americans are getting fatter, researchers have collected data by taking a random sample of 500 individuals, resulting in an average weight of 190 pounds. We want to compare this with the average weight from ten years ago, which was 185 pounds.
The hypothesis we are setting up will help us determine if there has been a significant increase in weight. Here's how we can set up the hypotheses:
Null Hypothesis (H0): This represents the statement of no effect or no difference. In this case, it would mean that the average weight has not increased. The null hypothesis can be written as:
[tex]H_0: \mu = 185[/tex]
where [tex]\mu[/tex] is the average weight of Americans.
Alternative Hypothesis (HA): This represents the statement that there is an effect or a difference. In this case, we are testing if the average weight has actually increased, implying that Americans are getting fatter. The alternative hypothesis can be written as:
[tex]H_A: \mu > 185[/tex]
Given the options provided, the correct choice would be:
- H0: [tex]\mu = 185[/tex], HA: [tex]\mu > 185[/tex]
This setup is used in a one-tailed hypothesis test where we specifically want to test if the average weight has increased beyond 185 pounds. This approach focuses on whether there is evidence to suggest that the mean weight now exceeds the previously average weight ten years ago.
In hypothesis testing, after setting up these hypotheses, researchers would typically use statistical methods to determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis. This involves determining a p-value and comparing it to a significance level (commonly 0.05) to make a decision.
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