Chp 18 Sampling (H2)

A sample has a more accurate mean and variance

It may not be possible to investigate the population

The units in a sample are independent of each other

The probability of success in a sample is constant

has an equal chance of being selected

has the same mean and variance

has 2 mutually exclusive outcome

is independently selected

is part of a normal distribution

N(1,1)

N(1,10)

N(10,1)

N(10,10)

Approximate $$\overline{X}\sim N\left(\mu,\frac{\sigma^2}{n}\right)$$  when X~B(n,p)

Approximate $$\overline{X}\sim N\left(\mu,\frac{\sigma^2}{n}\right)$$  when $$X\sim N\left(\mu,\sigma^2\right)$$  

Approximate $$\overline{X}\sim N\left(\mu,\frac{\sigma^2}{n}\right)$$  when X is an unknown distribution with known mean and variance

To convert any distribution to $$X\sim N\left(\mu,\sigma^2\right)$$

$$\overline{X}\sim N\left(6,\frac{\frac{1}{2}}{100}\right)$$ approximately by Central Limit Theorem

$$\overline{X}\sim N\left(3,\frac{3}{2}\right)$$ approximately by Central Limit Theorem

$$\overline{X}\sim N\left(3,\frac{\frac{3}{2}}{100}\right)$$ approximately by Central Limit Theorem

$$\overline{X}\sim N\left(3,\frac{\frac{3}{2}}{100}\right)$$  

$$\overline{X}\sim N\left(170,\frac{20}{50}\right)$$   approximately by Central Limit Theorem

$$\overline{X}\sim N\left(170,20\right)$$   approximately by Central Limit Theorem

$$\overline{X}\sim N\left(170,20\right)$$   

$$\overline{X}\sim N\left(170,\frac{20}{50}\right)$$  

Nothing can be done

$$\overline{X}\sim N\left(160,\frac{10}{10}\right)$$   approximately by Central Limit Theorem

$$\overline{X}\sim N\left(160,10\right)$$   approximately by Central Limit Theorem

$$\overline{X}\sim N\left(160,10\right)$$   

$$\overline{X}\sim N\left(160,\frac{10}{10}\right)$$  

Nothing can be done