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P1.T2.212. Difference between two means

David Harper CFA FRM

David Harper CFA FRM
Staff member
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AIM: Perform and interpret hypothesis tests for the difference between two means.

Questions:

212.1. We want to decide whether the average arithmetic return of Fund A is better than the average return of Fund B: the null hypothesis is that the true average difference is zero. For both fund, our sample is 60 months. Over this sample, the average return of Fund A was 2.0% with a standard deviation of 3.0%; the average return of Fund B was only 1.0% with standard deviation of 2.0%. With 95% confidence, do we reject the null hypothesis (i.e., fail to accept) and decide that the average return of Fund A was truly better?

a. No, the t-statistic is only 0.465
b. No, the t-statistic is only 1.465
c. Yes, the t-statistic is 2.148
d. Yes, the t-statistic is 5.359

212.2. The average hourly earnings among a sample of 1,500 men is $22.00 with a sample standard deviation of $9.00. The average hourly earnings among a sample of 1,000 women is $20.00 with a sample standard deviation of $6.00. What is the 95% confidence interval for the (two-sided) difference in average earnings between men and women?

a. $0.04 to $3.96
b. $1.41 to $2.59
c. $1.70 to $2.30
d. $1.83 to $2.17

212.3. A credit rating agency wants to compare the difference in default rates between structured notes in two speculative rating categories: SF B versus SF CCC. The default rate among a sample of 1,800 SF B-rated obligors was 5.0%, compared to the default rate among a sample of 1,000 SF CCC-rated obligors was 8.0%. Default is characterized by a Bernoulli random variable. What is the 95% confidence interval for the difference in default rates?

a. 2.97% to 3.04%
b. 2.11% to 3.89%
c. 1.75% to 4.25%
d. 1.04% to 4.96%

Answers:
 

ShaktiRathore

Well-Known Member
Subscriber
Hi,
Difference of sample variables d=x1-x2
Var(d)=var(x1)+var(x2)=81+36=117
Sd of d=sqrt(Var(d)=sqrt(117)=popln sd (assume)
Std error of sample differences=pop sd/sqrt(1000+1500)=sqrt(117)/50=.21633
CI is mean of diff+/-2*Std error of d~2+/-2*Std error~2-/+.432~1.568 -2.432 which implies option B as this interval lies within option B interval.

Thanks
 
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