Question
Asked Jan 18, 2020
1 views

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?

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

Image Transcriptionclose

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

fullscreen
check_circle

Expert Answer

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...

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Statistics

Other

Related Statistics Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: Durations of Pregnancies The lengths of pregnancies are normally distributed with a mean of 268 days...

A: a)The random variable x represents the duration of the pregnancy.

question_answer

Q: Flight Departure Delays Compare the three samples using means, medians, and standard deviations.

A: Step-by-step procedure to obtain the mean, median, and standard deviation using the MINITAB software...

question_answer

Q: IQ Scores. In Exercises,find the indicated IQ score, and round to the nearest whole number. The grap...

A: The random variable x represents the IQ score of adults.The area under the normal curve represents t...

question_answer

Q: The following table shows 40 different startup companies' first hour customers, sorted and arranged ...

A: The formula for finding the percentile p of the dataset is n*(p/100). Here, n is the size of the dat...

question_answer

Q: In Exercises, use the same population of {4, 5, 9} that was used in Examples 1 and 2. As in Examples...

A: a)The notation p represents the population variance.The formula to find the population proportion of...

question_answer

Q: Births There are about 11,000 births each day in the United States, and the proportion of boys born ...

A: a)Here, the samples of the same size are taken from the same population every day.

question_answer

Q: One-Way ANOVA In general, what is one-way analysis of variance used for?

A: In this case, we need find the use of the one-way analysis of variance.

question_answer

Q: Internet and Nobel Laureates Find the best predicted Nobel Laureate rate for Japan, which has 79.1 I...

A: Regression:The regression analysis is conducted here by using EXCEL. The software procedure is given...

question_answer

Q: Lemons and Car Crashes Using the listed lemon/crash data, find the best predicted crash fatality rat...

A: Regression:The regression analysis is conducted here by using EXCEL. The software procedure is given...