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Answer :
It seems there is a misunderstanding with the statement of the null and alternative hypotheses. In hypothesis testing, the typical approach is to set a null hypothesis (denoted as [tex]H_0[/tex]) and an alternative hypothesis (denoted as [tex]H_a[/tex]) that are mutually exclusive.
Let's correct the hypotheses setup for the problem described:
Null Hypothesis ([tex]H_0[/tex]): The null hypothesis would propose that the proportion of men who weigh more than 195 pounds is equal to a specific value. However, since specific weight details are not given in the question, this hypothesis would typically maintain a condition of equality.
Alternative Hypothesis ([tex]H_a[/tex]): The alternative hypothesis relates to what you aim to prove. If you want to find out if the average weight is less than 195 pounds, then the alternative hypothesis should reflect that.
[tex]H_0: \mu \geq 195 \text{ pounds}[/tex]
[tex]H_a: \mu < 195 \text{ pounds}[/tex]
The null hypothesis is that the average (mean weight [tex]\mu[/tex]) is equal to or greater than 195 pounds, while the alternative hypothesis is that [tex]\mu[/tex] is less than 195 pounds.
The goal of hypothesis testing is to use sample data to determine whether to reject the null hypothesis in favor of the alternative hypothesis. If the sample provides enough evidence that the average weight is less than 195 pounds, you would reject the null hypothesis.
The steps to perform this hypothesis test typically include:
- Collecting a sample of men's weights.
- Calculating the sample mean and standard deviation.
- Using a statistical test (like a t-test or z-test) to compare the sample mean to 195 pounds.
- Making a decision to accept or reject the null hypothesis based on the test results and a predefined significance level, usually 0.05 (5%).
Remember, the null hypothesis is never accepted as true; it is either rejected or not rejected based on the evidence collected during an experiment or survey.
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