Answer:
Is the number of tosses for each coin enough for the sampling distribution of the difference in sample proportions PA-PB to be approximately normal?
b. No, 20 tosses for coin A is enough, but 20 tosses for coin B is not enough.
Step-by-step explanation:
a) Data and Calculations:
The probability of coin A landing tails-side up = 0.5
The proportion of times coin A lands tails-side up (PA) = 20 * 0.5 = 10
Therefore, the probability of coin A landing heads-side up = 0.5 (1 - 0.5)
And the proportion of times that coin A lands heads-side up = 20 * 0.5 = 10.
The proportion on either side is equally distributed.
This is why 20 tosses for coin A is enough, since the sample proportions PA is approximately normal, symmetric, and equally distributed. There will be equal amounts of 10 tosses (0.5 *20) for either heads-side up or tails-side up.
For coin B, the probability of landing tails-side up = 0.8
The proportion of times coin B lands tails-side up (PB) = 20 * 0.8 = 16
Therefore, the probability of coin B landing heads-side up = 0.2 (1 - 0-.8)
The proportion on either side is not equally distributed, but skewed.
This is why 20 tosses for coin B is not enough, since the sample proportions PB is not approximately normal, symmetric, and equally distributed. There will be 16 tosses landing tails-side up (0.8*20) and only 4 tosses landing heads-side up (0.2*20).
Where,
