Answered: A stock analyst wondered whether the…

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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A stock analyst wondered whether the mean rate of return of financial, energy, and utility stocks differed over the past 5 years. He obtained a simple random sample of eight companies from each of the three sectors and obtained the 5-year rates of return shown in the accompanying table (in percent). Complete questions below.

Click the icon to view the data table.

Financial	Energy	Utilities

10.73	12.89	11.88
15.05	13.91	5.76
17.21	6.33	13.67
5.07	11.23	9.90
19.50	18.79	3.95
8.16	20.73	3.44
10.45	9.60	7.11
6.75	17.40	15.70

(a) State the null and alternative hypotheses. Choose the correct answer below.

H0: μfinancial=μenergy=μutilities

and H1: at least one of the means is different

H0: μfinancial=μenergy=μutilities

and H1: μfinancial<μenergy<μutilities

H0: at least one of the means is different

and H1: μfinancial=μenergy=μutilities

H0: μfinancial=μenergy

and H1: the means are different

(b) Normal probability plots indicate that the sample data come from normal populations. Are the requirements to use the one-way ANOVA procedure satisfied?

No, because the largest sample standard deviation is more than twice the smallest sample standard deviation.

Yes, because there are

k=3

simple random samples, one from each of k populations, the k samples are independent of each other, and the populations are normally distributed and have different variances.

No, because there are

k=3

simple random samples, one from each of k populations, the k samples are independent of each other, and the populations are normally distributed and have the same variance.

Yes, because there are

k=3

simple random samples, one from each of k populations, the k samples are independent of each other, and the populations are normally distributed and have the same variance.

α=0.05

level of significance?

Use technology to find the F-test statistic for this data set.

F0=nothing

(Round to two decimal places as needed.)

Determine the P-value and state the appropriate conclusion below.

Since the P-value is

nothing,

there

▼

is not

enough evidence to reject the null hypothesis. Thus, we

▼

can

cannot

conclude that the mean rates of return are different at the

α=0.05

level of significance.

(Round to three decimal places as needed.)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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