Objective
I am going to compare the prices in the South Atlantic States (Group 1) to the prices in the East and West South Central States (Group 2). The question to answer is if the prices in the south are lower than in other regions.
Conditions and Rejection Criteria
The test is the comparison of the mean values of two groups: houses in the South Atlantic States and the East and West South Central States. The sample size is 8 houses prices in each of the group, total 16 observations.
The research question is interpreted into hypothesis. The null hypothesis H0 states that the mean house price in south states is the same as the mean price in the East and West South Central States, or H0: μS=μEW.
The alternate hypothesis is opposite to the null H1: the mean house prices in the south are lower, or H1: μS<μEW. The data will be tested at 0.05 significance level.
Since the alternate hypothesis supposes that one mean is higher than the other, one-way independent sample t-test is applied.
The decision is made basing on the calculated t-test value, which is compared to the tabulated t-value (tcritical). The tcritical value is chosen basing on the chosen significance level (0.05), and the number of degrees of freedom, which calculated: f = n – 2. For the presented case, tcritical(0.95, 14). If t < tcritical., then null hypothesis is accepted, and the alternate hypothesis is rejected. If t> tcritical, we have to reject the null hypothesis and accept the alternate hypothesis.
Sample Size
The sample size is n = 16, which is 8 for the south states and 8 for the East and West South Central states. The sample size is determined by the states that belong to each group.
Descriptive Statistics
The descriptive statistics of the household prices in South and East & West South Central states
The normality of data can be confirmed by observation of the skewness and kurtosis values. For the normal distribution, skewness is close to 0, and kurtosis does not exceed 3. For both groups, the skewness values are around 1, and the kurtosis values are close to 0. This is a proof that the data are normally distributed, and the standard independent sample t-test can be applied.
Test Statistics
The test statistics calculates:
t=|μS-μEW|sc;
sc=sS2+sEW2.
Calculations:
sc=14067.492+65356.532=66853.3
t=|121200-182487.5|66853.3=0.91;
The decision is made by comparing tcritical(0.95;14) and the calculated t-value. tcritical(0.95;14) = 1.76 (taken from the table with t-critical values). The critical t-value is the rejection criteria. Comparing t(0.95;14) and t, t(0.95;14) > t (0.91 < 1.76). Therefore, the null hypothesis is true and the mean prices of the two groups of states are equal.
Conclusion
The statistical test proved that the mean houses prices in the south states are the same as in East & West Central states. There are not enough evidence that the prices differ significantly.
