AIMs: Define, interpret, and calculate the t-statistic. Define, calculate, and interpret a confidence interval.
Questions:
209.1. Nine (9) companies among a random sample of 60 companies defaulted. The companies were each in the same highly speculative credit rating category: statistically, they represent a random sample from the population of CCC-rated companies. The rating agency contends that the historical (population) default rate for this category is 10.0%, in contrast to the 15.0% default rate observed in the sample. Is there statistical evidence, with any high confidence, that the true default rate is different than 10.0%; i.e., if the null hypothesis is that the true default rate is 10.0%, can we reject the null?
a. No, the t-statistic is 0.39
b. No, the t-statistic is 1.08
c. Yes, the t-statistic is 1.74
d. Yes, the t-statistic is 23.53
209.2. Over the last two years, a fund produced an average monthly return of +3.0% but with monthly volatility of 10.0%. That is, assume the random sample size (n) is 24, with mean of 3.0% and sigma of 10.0%. Are the returns statistically significant; in other words, can we decide the true mean return is great than zero with 95% confidence?
a. No, the t-statistic is 0.85
b. No, the t-statistic is 1.47
c. Yes, the t-statistic is 2.55
d. Yes, the t-statistic is 3.83
209.3. Assume the frequency of internal fraud (an operational risk event type) occurrences per year is characterized by a Poisson distribution. Among a sample of 43 companies, the mean frequency is 11.0 with a sample standard deviation of 4.0. What is the 90% confidence interval of the population's mean frequency?
a. 10.0 to 12.0
b. 8.8 to 13.2
c. 7.5 to 14.5
d. Need more information (Poisson parameter)
Answers:
Questions:
209.1. Nine (9) companies among a random sample of 60 companies defaulted. The companies were each in the same highly speculative credit rating category: statistically, they represent a random sample from the population of CCC-rated companies. The rating agency contends that the historical (population) default rate for this category is 10.0%, in contrast to the 15.0% default rate observed in the sample. Is there statistical evidence, with any high confidence, that the true default rate is different than 10.0%; i.e., if the null hypothesis is that the true default rate is 10.0%, can we reject the null?
a. No, the t-statistic is 0.39
b. No, the t-statistic is 1.08
c. Yes, the t-statistic is 1.74
d. Yes, the t-statistic is 23.53
209.2. Over the last two years, a fund produced an average monthly return of +3.0% but with monthly volatility of 10.0%. That is, assume the random sample size (n) is 24, with mean of 3.0% and sigma of 10.0%. Are the returns statistically significant; in other words, can we decide the true mean return is great than zero with 95% confidence?
a. No, the t-statistic is 0.85
b. No, the t-statistic is 1.47
c. Yes, the t-statistic is 2.55
d. Yes, the t-statistic is 3.83
209.3. Assume the frequency of internal fraud (an operational risk event type) occurrences per year is characterized by a Poisson distribution. Among a sample of 43 companies, the mean frequency is 11.0 with a sample standard deviation of 4.0. What is the 90% confidence interval of the population's mean frequency?
a. 10.0 to 12.0
b. 8.8 to 13.2
c. 7.5 to 14.5
d. Need more information (Poisson parameter)
Answers:
