Then, for the following two examples, determine the null and alternative as well as state which one represents the claim. State what type of test will be completed: left-tailed, right-tailed, or two-tailed.
The average score of the first exam for the class is an 81%.Claim 2: The average price for a gallon of gas is more than $3.00.
It depends on what question you are asking.
Ho: mean = 81%
Ha: mean ≠ 81%
Two-tailed
Ho: mean = $3.00
Ha: mean > $3.00
I'm not sure what you mean by right-tailed or left-tailed. I don't use those specific terms.
Upon further thought, right-tailed may be the equivalent to positively skewed (deviant scores at higher values). If so, the second Ha would be right-tailed.
The mean is influenced by deviant scores, like a fulcrum (balance point). Thus Ha for "more than $3.00" would be looking for a higher mean and "right-tailed."
To determine the null and alternative hypotheses for the given examples, we need to understand the claim being made and how it relates to the statistical test.
Example 1:
Null Hypothesis (H0): The average score of the first exam for the class is 81%.
Alternative Hypothesis (Ha): The average score of the first exam for the class is not 81%.
Claim: The claim in this case is that the average score of the first exam for the class is different from 81%.
Type of Test: This is a two-tailed test because the alternative hypothesis is looking for a difference from the null hypothesis in any direction.
Example 2:
Null Hypothesis (H0): The average price for a gallon of gas is $3.00.
Alternative Hypothesis (Ha): The average price for a gallon of gas is more than $3.00.
Claim: The claim in this case is that the average price for a gallon of gas is more than $3.00.
Type of Test: This is a right-tailed test because the alternative hypothesis is looking for a higher value than the null hypothesis.
In summary:
Example 1 - Two-tailed test with the claim of a difference in the average score of the first exam for the class.
Example 2 - Right-tailed test with the claim of the average price for a gallon of gas being more than $3.00.