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.

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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.
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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.
 
 
A.
H0: μfinancial=μenergy=μutilities
and H1: at least one of the means is different
 
B.
H0: μfinancial=μenergy=μutilities
and H1: μfinancial<μenergy<μutilities
 
C.
H0: at least one of the means is different
and H1: μfinancial=μenergy=μutilities
 
D.
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?
 
A.
​No, because the largest sample standard deviation is more than twice the smallest sample standard deviation.
 
B.
​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.
 
C.
​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.
 
D.
​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.
 
​(c) Are the mean rates of return different at the
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
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.)
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