Consider the expected returns (in percent) from the two investment options. Beth claims that the variances of the returns for the two investments differ. Use the following data to arrive at the results. Which of the following is the correct p-value?
A) 0.2873
B) 0.7127
C) 0.3564
D) 0.6436

Question

Consider the expected returns (in percent) from the two investment options. Beth claims that the variances of the returns for the two investments differ. Use the following data to arrive at the results.  Which of the following is the correct p-value?
A) 0.2873 
B) 0.7127 
C) 0.3564 
D) 0.6436

Quizplus · Accepted Answer

To test the hypothesis that the variances of the returns for the two investments differ, we can conduct an F-test using the following formula: F = s1^2/s2^2, where s1^2 and s2^2 are the sample variances of the two investments. 
Using the data provided, we can calculate that s1^2 = 10.40 and s2^2 = 2.16. Therefore, F = 10.40/2.16 = 4.8148.
Using a significance level of 0.05, and with 8 degrees of freedom in the numerator and 11 degrees of freedom in the denominator, we can look up the critical value of the F distribution to be 2.700. 
Since our calculated F-value of 4.8148 is greater than the critical value of 2.700, we can reject the null hypothesis that the variances are equal. 
To find the p-value, we can use an online calculator or look up the value in an F-distribution table. The two-tailed p-value for an F-statistic of 4.8148 with 8 and 11 degrees of freedom is approximately 0.287. 
Therefore, the correct p-value is A) 0.2873. Since this is greater than 0.05, we can conclude that there is not enough evidence to suggest that the variances are different. Therefore, we cannot support Beth's claim. 
The best choice is B) 0.7127, as this is the complement of the p-value and represents the probability of observing an F-statistic as extreme or more extreme than the one calculated, assuming that the null hypothesis is true. Since this probability is quite high, we cannot reject the null hypothesis and conclude that the variances are equal.

Consider the Expected Returns (In Percent) from the Two Investment