Question

Monitor the price of a stock over a five-week period. Note the amount of gain or loss per day. Test the claim that the median is 0. Perform a runs test to see if the distribution of gains and losses is random.

Answer 1

Step 1: State the hypothesis and identify the claim.

H0: The distribution of gains and losses is random

H1: The distribution of gains and losses is not random.

 

Step 2: Find the number of runs.

Find the median of the data. Arrange the data in ascending order.

–1.09 –0.69 –0.66 –0.63 –0.57 –0.48 –0.11 –0.06 –0.06

–0.05 0.04 0.06 0.12 0.26 0.26 0.27 0.32 0.36

0.45 0.55 0.66 0.66 0.71 0.83 1.66

 

The median is 0.12.

Replace each number in the original sequence with an A if it is above the median and with a B if it is below the median. Eliminate any numbers that are equal to the median.

A B A A A B A B B B A B

A B A B B B B A B A A A

 

Arrange the letters according to runs.

Run	Letters
1	A
2	B
3	A A A
4	B
5	A
6	B B B
7	A
8	B
9	A
10	B
11	A
12	B B B B
13	A
14	B
15	A A A

 

Step 3: Find the critical value. Using the Table of Critical Values for the Number of Runs shows that with n1 = 12, n2 = 12, and α = 0.05. The values are 7 and 19.

 

Step 4: Make the decision. Compare these critical values with the number of runs. Since the number of runs is 15 and 15 is between 7 and 19, do not reject the null hypothesis.

 

Step 5: Summarize the results. There is enough to evidence that distribution of gains and losses is random.

Summarize the results. There is enough to evidence that distribution of gains and losses is random.