Question

A random sample of 30 stocks was selected from each of the three major U.S. exchanges and their performance over the previous year was noted. The median performance for all 90 stocks was noted and the following table constructed, Exchange Median New York 18 American 17 NASDAQ 10 Was there a significant difference in the performance of stocks on the three exchanges during the previous year?

Answer 1

To Chi square test for independence is used to test the significance of the median.

Step 1: The hypothesis for the test is defined as;

Ho: There is no difference in medians (such that all the medians are equal).

Ha: There is a significant difference in medians (such that at least one median is different)

Step 2: The significance level for the test is,

Step 3: The Chi-Square test statistic is obtained as follow,

From the data provided, the observed frequencies are,

Observed frequencies
	New York	American	NASDAQ	Total
Above	18	17	10	45
Below	12	13	20	45
Total	30	30	30	90

Step 4: The expected values are obtained using the formula,

The expected values are,

Expected frequencies
	New York	American	NASDAQ
Above	15	15	15
Below	15	15	15

Step 5: Now the Chi-Square Value is obtained using the formula,

Step 6: The P-value for Chi-Square statistic is obtained using the chi square distribution table,

Step 7:

The null hypothesis is failed to reject. It can be stated now, there is no statistically significant difference between three medians at 5% significant level.