Cholesterol levels of adult males are approximately normally distributed with a mean of mg/dL and a listed standard deviation of . Some researchers claim that the standard deviation of cholesterol levels of adult males is less than . Suppose that we want to carry out a hypothesis test to see if the actual standard deviation of cholesterol levels of adult males is less than . State the null hypothesis and the alternative hypothesis that we would use for this test
To carry out a hypothesis test to see if the actual standard deviation of cholesterol levels of adult males is less than a certain value, we can set up the null hypothesis (H0) and the alternative hypothesis (Ha).
The null hypothesis (H0) states that the standard deviation of cholesterol levels of adult males is equal to or greater than the claimed value. In this case, the null hypothesis is:
H0: The standard deviation of cholesterol levels of adult males is greater than or equal to σ.
The alternative hypothesis (Ha) states that the standard deviation of cholesterol levels of adult males is less than the claimed value. In this case, the alternative hypothesis is:
Ha: The standard deviation of cholesterol levels of adult males is less than σ.
So, to summarize:
Null hypothesis (H0): The standard deviation of cholesterol levels of adult males is greater than or equal to σ.
Alternative hypothesis (Ha): The standard deviation of cholesterol levels of adult males is less than σ.