# Question: For a single toss of a balanced coin let x

For a single toss of a balanced coin, let x = 1 for a head and x = 0 for a tail.

a. Construct the probability distribution for x, and calculate its mean. (You can think of this as the population distribution corresponding to a very long sequence of tosses.)

b. The coin is flipped 10 times, yielding 6 heads and 4 tails. Construct the data distribution.

c. Each student in the class should flip a coin 10 times and find the proportion of heads. Collect the sample proportion of heads from each student. Summarize the simulated sampling distribution by constructing a plot of all the proportions obtained by the students. Describe the shape and variability of the sampling distribution compared to the distributions in parts a and b.

d. If you performed the experiment in part c a huge number of times, what would you expect to get for the (i) mean and (ii) standard deviation of the sample proportions?

a. Construct the probability distribution for x, and calculate its mean. (You can think of this as the population distribution corresponding to a very long sequence of tosses.)

b. The coin is flipped 10 times, yielding 6 heads and 4 tails. Construct the data distribution.

c. Each student in the class should flip a coin 10 times and find the proportion of heads. Collect the sample proportion of heads from each student. Summarize the simulated sampling distribution by constructing a plot of all the proportions obtained by the students. Describe the shape and variability of the sampling distribution compared to the distributions in parts a and b.

d. If you performed the experiment in part c a huge number of times, what would you expect to get for the (i) mean and (ii) standard deviation of the sample proportions?

## Answer to relevant Questions

Refer to the previous exercise. a. In part b, if the sampling distribution of the sample proportion had mean 0.409 and the standard deviation 0.008, give an interval of values within which the sample proportion will almost ...A study dealing with health care issues plans to take a sample survey of 1500 Americans to estimate the proportion who have health insurance and the mean dollar amount that Americans spent on health care this past year. a. ...Using the sample size formula n = [p̂ (1 - p̂)z2]/m2 for a proportion, explain the effect on n of (a) Increasing the confidence level and (b) Decreasing the margin of error. To encourage subjects to make honest responses on sensitive questions, the method of randomized response is often used. Let’s use your class to estimate the proportion that have had alcohol at a party. Before carrying out ...A national television network takes an exit poll of 1400 voters after each has cast a vote in a state gubernatorial election. Of them, 660 say they voted for the Democratic candidate and 740 say they voted for the Republican ...Post your question