Sampling Distributions for Proportions

The Gallup Poll asked a random sample of 1785 adults whether they attended church during the past week.  Let p-hat be the proportion of people in the sample who attended church.  A newspaper report claims that 40% of all U.S. adults went to church last week.  Suppose this claim is true. 
What is the mean of the sampling distribution of p-hat?

• 0.4
• 0.44
• 0.56
• 0.6

28% of all Woodrow students believe Monday will be snow day. You take a sample of 50 students and find that 15 of them believe Monday will be a snow day. What does 50 represent? 

• n
• P
• phat
• standard deviation

What happens to the shape of a sampling distribution of sample means as n increases?

• It becomes narrower (closer to the population's true mean) and bimodal.

• It becomes narrower (closer to the population's true mean) and more normal.

• It becomes wider (further from the population's true mean)and skewed right.

• It becomes wider (further to the population's true mean)and more normal.

When sampling from a population with proportion p, the distribution of sample proportions (p-hat) will vary. What will be the mean of all possible sample proportions?

• p

When sampling from a population with proportion p, the sample outcomes will vary.  Which of the following represents the standard deviation of the sampling distribution?

• p

30% of all dogs in a city are micro-chipped. In a sample of 500 dogs, what is the probability that less than 32% of dogs are micro-chipped?

• 0.2586

• 0.1587

• 0.8233

• 0.1398

• 0

Knowing that the result of flipping a coin is equally likely (that means, 50/50 chance of observing either outcome). If you flip a coin 500 times, what's the probability that at least 51% of them will be Tails.

• Essentially 0.

• 0.2891

• 0.3437

• 0.8512

• 0.8236

What is the standard deviation of the distribution?

• 1010
• 20
• 60
• √20

Your mail-order company advertises that it ships 90% of its orders within three working days. You select an SRS of 100 of the 5000 orders received in the past week for an audit.

What is the mean?

• 0.9

• 0.1

• 500

• 450

• 0.5

Your mail-order company advertises that it ships 90% of its orders within three working days. You select an SRS of 100 of the 5000 orders received in the past week for an audit.

What is the standard deviation?

• 0.04

• 0.004

• 0.3

• 0.03