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.
Claim 1: 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.
Here are the 3 kinds of tests
H0: mu <= x
HA: mu > x
H0: mu >= x
HA: mu < x
H0: mu = x
HA: mu ≠ x
The equals sign indicates the difference between the null and alternative hypotheses. The hypothesis with the = sign represents the claim, and is assumed accurate unless evidence points to it being false.
The null hypothesis is the one which shows "equal" values or "no change". The alternative hypothesis is stated as "greater than", "less than", or "not equal to".
Claim 1: H0 (claim): mu = 0.81
HA: mu ≠ 0.81
Claim 2: H0: mu <= 3
HA (claim): mu > 3
Note the way the claim was stated: "more than $3.00", not "$3.00 or more". This means that if the test shows no significant difference from $3.00, the null hypothesis should not be rejected.