At the end of 2008 the variance in the semiannual yields of

At the end of 2008, the variance in the semiannual yields of overseas government bond was 2 = .70. A group of bond investors met at that time to discuss future trends in overseas bond yields. Some expected the variability in overseas bond yields to increase and others took the opposite view. The following table shows the semiannual yields for 12 overseas countries as of March 6, 2009 (Barron\'s, March 9, 2009).

Click on the webfile logo to reference the data.

a. Compute the mean, variance, and standard deviation of the overseas bond yields as of March 6, 2009 (to 4 decimals).

b. What is the value of the population variance in the null hypothesis for this question? (to 2 decimals).

c. Use  = .05 to conduct the hypothesis test formulated in part (b). What is your conclusion?

We cannot conclude from the sample data that the variance in bond yields has changed from 2008.

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I need help with solving part B, thanks

Solution

b)

sigma^2 = 0.70, as given. [ANSWER]

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c)

Formulating the null and alternative hypotheses,              
              
Ho:   sigma   <=   0.7  
Ha:    sigma   >   0.7  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical chi^2, as alpha =    0.05   ,      
alpha =    0.05          
df = N - 1 =    11          
chi^2 (crit) =    19.67513757        
              
Getting the test statistic, as              
s = sample standard deviation =    0.8306          
sigmao = hypothesized standard deviation =    0.7          
n = sample size =    12          
              
              
Thus, chi^2 = (N - 1)(s/sigmao)^2 =    15.48746931          
********              
As chi^2 < chi^2(crit), then we FAIL TO REJECT THE NULL HYPOTHESIS.