Question

1. At the end of 2015, the variance in the semiannual yields of overseas governments bond was σ2 = 0.85. 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 other took the opposite view. The table below shows semiannual yields for 10 countries (March 2016). Country Yield (%) Country Yield (%) Belice 5 Chile 3.25 Honduras 10 Bolivia 6.05 Norway 1.25 Argentina 12.75 Greece 5.75 Colombia 3.77 Bulgaria 8.23 Tunisia 6.78 a. Compute the mean, variance, and standard deviation of the overseas bond yields as of March 2016. b. Develop hypotheses to test whether the sample data indicate that the variance in bond yields has changed from that at the end of 2015. c. Use level of significance = 5% to conduct the hypothesis in part (b). What is your conclusion?

Answer 1

At the end of 2015, the variance in the semiannual yields of overseas governments bond was σ2 = 0.85. 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 other took the opposite view. The table below shows semiannual yields for 10 countries (March 2016). Country Yield (%) Country Yield (%)

Belice 5

Chile 3.25

Honduras 10

Bolivia 6.05

Norway 1.25

Argentina 12.75

Greece 5.75

Colombia 3.77

Bulgaria 8.23

Tunisia 6.78

1. Compute the mean, variance, and standard deviation of the overseas bond yields as of March 2016.

n	10
mean	6.2830
sample standard deviation	3.3748
sample variance	11.3895

b. Develop hypotheses to test whether the sample data indicate that the variance in bond yields has changed from that at the end of 2015.

One sample variance test

= (9*11.3895) / 0.85=120.59

DF=10-1=9

c. Use level of significance = 5% to conduct the hypothesis in part (b). What is your conclusion?

Critical Chi square value at 0.05 level =(2.70, 19.02)

Calculated chi square = 120.59 falls in the critical region.

The null hypothesis is rejected.

At the 5% level of significance, we conclude that the variance in bond yields has changed from that at the end of 2015.