Question

A real state agent wishes to determine if there is a significant difference in the selling prices of homes in two Seattle suburbs. She took a sample of 41 homes from the first suburbs and found the average selling price from was $261,225. The standard deviation of all homes in that suburb is $5,602. She took a sample of 61 homes from the second suburb and the average selling price was $259,102. The standard deviation of all homes in the second suburb is $4,731. We are testing a null hypothesis of  against an alternative hypothesis of .

Find the value of the test statistic.

Answer 1

Here in this scenario our claim is that there is a significant difference in the selling prices of homes in two Seattle suburbs.

Now the sample information is given She took a sample of 41 homes from the first suburbs and found the average selling price from was $261,225. The standard deviation of all homes in that suburb is $5,602. She took a sample of 61 homes from the second suburb and the average selling price was $259,102. The standard deviation of all homes in the second suburb is $4,731.

Here we assumed that the population Variances are unequal.

Now to test this claim we need to use two sample t test because here the population standard deviations is unknown

We also assuming that the level of significance is 0.05 ( for illustration of test).

Further the test is performed at 0.05 level of significance as below,

The t critical value is calculated using t table or using Excel. At 75.912 degrees of freedom.

The value of the test Statistic is t cal = 1.995.

Please note that we assumed that the population Variances are unequal. ( If you Assuming that the population Variances are equal then the test Statistic formula is different).

Thank you.