Statistical hypothesis testing is a very important concept in statistics. There are steps to be followed in hypothesis testing, as shown below (Eberly College of Science, n.d.)
Formulation of the Null Hypothesis – this step involves stating of the null hypothesis, which states equality between the hypothesized value and a predicted value. In this case, it is the opposite of the alternative hypothesis.
H0: The average salary for all jobs in Minnesota is greater than or equal to $65,000.
H0: x ≥$65,000
Formulation of the Alternative Hypothesis –the alternative hypothesis is the opposite of the null hypothesis, which states that a value is less than, greater than, or not equal to a certain value. This is the claim for the given problem.
Ha: The average salary for all jobs in Minnesota is less than $65,000.
Ha: x <$65,000
Setting of level of significance α – the level of significance determines the Type I error of the test. In this case, α = 0.05 as per given.
Determining the test procedure - in this case, the test that will be performed is the t-test, given that the population has an unknown σ. Since the alternative hypothesis states a “less than” claim, the test is one-tailed (left-tailed).
Construction of a decision rule – A decision rule determines whether the null hypothesis will be rejected or not. There are two ways to do this: the critical value method or the p-value method. The p-value is far easier to compare since it only involves one rule, unlike the critical value which changes depending on the alternative hypothesis. However, computation of the p-value is more complicated.
In this test, the decision rule is to reject H0 if p-value is less than α. Alternatively, reject H0 if test statistic is less than -1.645.
Computation of the test statistic – there are two methods to compute the test statistic, a value which will be compared to the tabular value. In the critical value test, the mean of the value as well as their standard deviation will first be determined. Afterwards, it will be plugged in in the following formula, as shown below:
tval= x-μsn= 62306.13-6500019149.21364=-2.6840
The p-value can also be computed. Since the computation of the p-value is a bit complicated, it can be looked up on statistical software instead. The computed p-value is 0.0038.
Coming up with a decision – the null hypothesis is rejected or accepted based on the decision rule made earlier. Since -2.6840 < -1.645 and 0.0038 < 0.05, the null hypothesis is rejected.
Arriving at a conclusion – since the null hypothesis is rejected, we can accept the alternative hypothesis that the average salary in Minnesota is indeed less than $65,000, which supports the claim.
Reference
“The 7 Step Process of Statistical Hypothesis Testing” (n.d.). Eberly College of Science. Retrieved from https://onlinecourses.science.psu.edu/stat502/node/139
