Estimators, bias and the sampling distribution of the mean Quiz

1. A sample of 5 values has $\sum x=60$ and $\sum x^2=760$. What is the unbiased estimate of the population variance?

• A. $10$
• B. $8$
• C. $40$
• D. $12.5$

2. $X\sim N(40,36)$. A random sample of 9 is taken. What is the distribution of $\bar X$?

• A. $N(40,36)$
• B. $N(40,12)$
• C. $N(4.44,4)$
• D. $N(40,4)$

3. Which is the standard error of $\bar X$ for $n=25$ and $\sigma=10$?

• A. $0.4$
• B. $4$
• C. $2$
• D. $20$

4. An estimator $T$ has $E(T)=\frac{4\theta}{5}$. What is its bias?

• A. $+\frac{\theta}{5}$
• B. $-\frac{\theta}{5}$
• C. $0$
• D. $\frac{4\theta}{5}$

5. To halve the standard error of the sample mean, the sample size must be multiplied by:

• A. $2$
• B. $\sqrt2$
• C. $4$
• D. $8$