I am confused on what statistic test I should perform. I think it should be the t-test, which I have provided below. If the t-test is correct, how do I decide if I need to reject the null hypothesis. I get really confused on these things.
Null Hypothesis: The State of South Carolina cost of living increases for active employees are less than or equal to the average cost of living increases of the Social Security Administration provided during the years 1996-2007. (H0: ¦ÌX ¡Ý ¦ÌY).
Alternative Hypothesis: The State of South Carolina cost of living increases for active employees are greater than the average cost of living increases the Social Security Administration provided during the years 1996-2007. (Ha: ¦ÌX < ¦ÌY).
South Carolina Social Security
Mean 0.022833333 0.025916667
Variance 0.000163606 6.62652E-05
Observations 12 12
Pooled Variance 0.000114936
Hypothesized Mean Difference 0
df 22
t Stat -0.704480227
P(T<=t) one-tail 0.244262456
t Critical one-tail 1.717144335
P(T<=t) two-tail 0.488524913
t Critical two-tail 2.073873058
You can use a one-tailed t-test, assuming that you have the means and variance or standard deviation for both groups. Most studies use P ≤ .01 to reject the null hypothesis.
I hope this helps. Thanks for asking.
To determine if you should reject the null hypothesis using the t-test, you need to compare the calculated t-statistic to the critical t-value.
In this case, the t-statistic is given as -0.704480227. You can see that the t-test is a one-tailed test because the alternative hypothesis is specified as ¦ÌX < ¦ÌY.
To determine if you should reject the null hypothesis, you can compare the t-statistic to the critical t-value. The critical t-value for a one-tailed test with a significance level of 0.05 (commonly used) and 22 degrees of freedom is approximately 1.717144335.
Since the calculated t-statistic (-0.704480227) is smaller in magnitude than the critical t-value (1.717144335), we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that the cost of living increases for active employees in South Carolina are greater than the average cost of living increases provided by the Social Security Administration during the years 1996-2007.