What happens to the standard deviation of p̂ as the sample size increases? If the sample size is increased by a factor of 4, what happens to the standard deviation of p̂?

Variability in Baseball Suppose, during the course of a typical season, a batter has 500 at-bats. This means the player has the opportunity to get a hit 500 times during the course of a season. Further, suppose a batter is a career 0.280 hitter (he averages 280 hits every 1000 at-bats or he has 280 successes in 1000 trials of the experiment), so the population proportion of hits is 0.280.

b. Would it be unusual for a player who is a career 0.280 hitter to have a season in which he hits at least 0.310?

Describe the circumstances under which the shape of the sampling distribution of p̂ is approximately normal.

According to the National Center for Health Statistics, 22.4% of adults are smokers. A random sample of 300 adults is obtained.

a. Describe the sampling distribution of p̂, the sample proportion of adults who smoke.

True or False: The population proportion and sample proportion always have the same value.

A simple random sample of size n = 1000 is obtained from a population whose size is N = 1,000,000 and whose population proportion with a specified characteristic is p = 0.35.

c. What is the probability of obtaining x = 320 or fewer individuals with the characteristic?

A simple random sample of size n = 1460 is obtained from a population whose size is N = 1,500,000 and whose population proportion with a specified characteristic is p = 0.42.

c. What is the probability of obtaining x = 584 or fewer individuals with the characteristic?

Reincarnation Suppose 21% of all American teens (age 13–17 years) believe in reincarnation.

b. Explain why Bob’s sample of 100 randomly selected American teens might result in 18 who believe in reincarnation, while Alicia’s independent sample of 100 randomly selected American teens might result in 22 who believe in reincarnation.

Reincarnation Suppose 21% of all American teens (age 13–17 years) believe in reincarnation.

d. In a survey of 100 American teens, how many would you expect to believe in reincarnation?