Test the sequence for randomness about the median. Use ? = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. H0: The numbers are not randomly mixed about the median. H1: The numbers are randomly mixed about the median.H0: The numbers are randomly mixed about the median. H1: The numbers are not randomly mixed about the median. H0: The numbers are randomly mixed about the mean. H1: The numbers are not randomly mixed about the mean.H0: The numbers are not randomly mixed about the mean. H1: The numbers are randomly mixed about the mean. (b) Find the sample test statistic R, the number of runs. R = (c) Find the upper and lower critical values in the Critical Values for Number of Runs R table. c1=c2= (d) Conclude the test. At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (e) Interpret the conclusion in the context of the application. Reject the null hypothesis, there is sufficient evidence that the sequence of returns is not random about the median.Fail to reject the null hypothesis, there is insufficient evidence that the sequence of returns is not random about the mean. Fail to reject the null hypothesis, there is insufficient evidence that the sequence of returns is not random about the median.Reject the null hypothesis, there is sufficient evidence that the sequence of returns is not random about the mean.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Many economists and financial experts claim that the price level of a stock or bond is not random, but the price changes tend to follow a random sequence over time. The following data represent annual percentage returns on a stock index for a sequence of recent years.

12.4

10.8

−0.6

35.6

21.4

31.2

23.4

−10.8

−11.6

−21.2

10.6

Test the sequence for randomness about the median. Use ? = 0.05.

(a)

What is the level of significance?

State the null and alternate hypotheses.

H₀: The numbers are not randomly mixed about the median.
H₁: The numbers are randomly mixed about the median.H₀: The numbers are randomly mixed about the median.
H₁: The numbers are not randomly mixed about the median. H₀: The numbers are randomly mixed about the mean.
H₁: The numbers are not randomly mixed about the mean.H₀: The numbers are not randomly mixed about the mean.
H₁: The numbers are randomly mixed about the mean.

(b)

Find the sample test statistic R, the number of runs.

R =

(c)

Find the upper and lower critical values in the Critical Values for Number of Runs R table.

c₁=c₂=

(d)

Conclude the test.

At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e)

Interpret the conclusion in the context of the application.

Reject the null hypothesis, there is sufficient evidence that the sequence of returns is not random about the median.Fail to reject the null hypothesis, there is insufficient evidence that the sequence of returns is not random about the mean. Fail to reject the null hypothesis, there is insufficient evidence that the sequence of returns is not random about the median.Reject the null hypothesis, there is sufficient evidence that the sequence of returns is not random about the mean.

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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