Question

Your partner believes that the average house price in Illinois is the same as the average house price in California. Your team randomly selects 9 houses in California. The sample average for California is $200K. The sample standard deviation for California is $90K. You use the same data for Illinois. Specifically, for Illinois your sample size is 4. Sample average for Illinois is $250K. The sample standard deviation for Illinois is $60K. Test the hypothesis that the average house price in Illinois is the same as the average house price in California against the alternative that they are not the same (two-sided). Use alpha 5%. Below provide the test statistic up to 3 decimal points.

Answer 1

As we are testing here whether the house price in Illinois is the same as the average house price in California, therefore the null and the alternate hypothesis here are given as:

According to the given sample statistics, the standard error is first computed here as:

Now the test statistic here is computed as:

Now for n₁ + n₂ - 2 = 11 degrees of freedom, we get the p-value here as:

p = 2P( t₁₁ < -1.1785 ) = 2*0.1317 = 0.2634

As the p-value here is 0.2634 > 0.05 which is the level of significance, therefore the test is not significant and we cannot reject the null hypothesis here. therefore we dont have sufficient evidence here that the two means are different.