Question

Asked Jan 18, 2020

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Stock Market: Testing for Randomness Above and Below the Median Listed below are the annual high values of the Dow Jones Industrial Average for a recent sequence of years. Find the median, then test for randomness below and above the median. What does the result suggest about the stock market as an investment consideration?

Step 1

**Note:** In this context, the software usage is not mentioned. In order to obtain the run test statistic, we have used MINITAB software to solve the problem.

*Median:*

Arrange the data in the ascending order.

842, 882, 892, 898, 908, 943, 951, 969, 969, 985, 995, 1000, 1000, 1015, 1024, 1036, 1052, 1071, 1287, 1287, 1553, 1956, 2184, 2722, 2791, 3000, 3169, 3413, 3794, 3978, 5216, 6561, 8259, 9374, 10454, 10580, 10635, 10855, 10941, 11350, 11401, 11568, 11625, 12464, 12929, 13279, 13589, 14198, 16577 and 18054.

The sample size is 50. That is, even.

Then, the median is the average of the two middle values. That is, 2,895.5 (=(2,791+3,000)/2).

Thus, the median of the annual high values of the Dow Jones industrial average for a recent sequence of years is 2,895.5.

Step 2

*Test for randomness*:

The observations that are above the median are 3000, 3169, 3413, 3794, 3978, 5216, 6561, 8259, 9374, 10454, 10580, 10635, 10855, 10941, 11350, 11401, 11568, 11625, 12464, 12929, 13279, 13589, 14198, 16577 and 18054. That is, n1=25.

The observations that are below the median are 842, 882, 892, 898, 908, 943, 951, 969, 969, 985, 995, 1000, 1000, 1015, 1024, 1036, 1052, 1071, 1287, 1287, 1553, 1956, 2184, 2722 and 2791. That is, n2=25.

Step 3

The hypotheses are given below:

*Null hypothesis:*

H0: The annual high values are random.

*Alterna...*

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