Question

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).

Financial   Energy   Utilities
10.76   12.89   11.88
15.05   13.91   5.76
17.21   6.43   13.67
5.03   11.23   9.90
19.50   18.79   3.95
8.21   20.73   3.44
10.38   9.60   7.11
6.52   17.40   15.70

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

A.H0: μfinancial=μenergy=μutilities H1: μfinancial<μenergy<μutilities

B. H0: μfinancial=μenergy=μutilities H1: at least one of the means is different Your answer is correct.

C. H0: at least one of the means is different H1: μfinancial=μenergy=μutilities

D. H0: μfinancial=μenergy 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 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.

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 the same variance.

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

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 different variances.

​(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=2.06

​(Round to two decimal places as​ needed.)

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

Since the​ P-value is __?__ there

▼

is

is not

enough evidence to reject the null hypothesis.​ Thus, we

▼

cannot

can

conclude that the mean rates of return are different at the α=0.05 level of significance.

​(Round to three decimal places as​ needed.)

Answer 1

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

B. H0: μfinancial=μenergy=μutilities H1: at least one of the means is different Your answer is correct.

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

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 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.

The calculated F =2.06.

(d) Determine the​ P-value and state the appropriate conclusion below. Since the​ P-value is 0.153?

IS NOT there enough evidence to reject the null hypothesis.​

Thus, we CANNOT conclude that the mean rates of return are different at the α=0.05 level of significance.