Suppose all left-handed people are excluded from a sample. What is this an example of?

The proportion of left-handed people in the general population is about 0.1. Suppose a random sample of 225 people is observed.

1. What is the sampling distribution of the sample proportion (p-hat) ? In other words, what can we say about the behavior of the different possible values of the sample proportion that we can get when we take such a sample?

(Note: normal approximation is valid because. 1 (225) = 22.5 and. 9 (225) = 202.5 are both more than 10.)

2. Since the sample proportion has a normal distribution, its values follow the Standard Deviation Rule. What interval is almost certain (probability. 997) to contain the sample proportion of left-handed people?

3. In a sample of 225 people, would it be unusual to find that 40 people in the sample are left-handed?

4. Find the approximate probability of at least 27 in 225 (proportion. 12) being left-handed. In other words, what is P (p-hat? 0.12) ?

Guidance: Note that 0.12 is exactly 1 standard deviation (0.02) above the mean (0.1). Now use the Standard Deviation Rule.

Answer: Selection Bias