Question

Two coins, a and b, each have a side for heads and a side for tails. When coin a is tossed, the probability it will land tails-side up is 0. 5. When coin b is tossed, the probability it will land tails-side up is 0. 8. Both coins will be tossed 20 times. Let pˆa represent the proportion of times coin a lands tails-side up, and let pˆb represent the proportion of times coin b lands tails-side up. Is the number of tosses for each coin enough for the sampling distribution of the difference in sample proportions pˆa−pˆb to be approximately normal?.

Answer 1

The true statement about the sample proportions of coins A and B is (b) No, 20 tosses for coin A is enough, but 20 tosses for coin B is not enough.

Coin A

--- the probability of landing tails-side up

--- number of toss

Coin B

--- the probability of landing tails-side up

--- number of toss

Start by calculating the expected number of times both coins land on either sides.

This means that, there will an expected equal amount of outcomes for the heads and tails of coin A.

Hence, 20 tosses is enough for coin A because the proportion is equally distributed and approximately normal.

This means that, there won't be an expected equal amount of outcomes for the heads and tails of coin B.

Hence, 20 tosses is not enough for coin B because the proportion is neither equally distributed nor approximately normal.

So, the correct option is (b)

Step-by-step explanation:

a. Yes, 20 tosses for each coin is enough.

b. No, 20 tosses for coin A is enough, but 20 tosses for coin B is not enough.

c. No, 20 tosses for coin A is not enough, but 20 tosses for coin B is enough.

d. No, 20 tosses is not enough for either coin.

e. There is not enough information given to determine it 20 tosses is enough.