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

According to the Center for Disease Control, 93% of children entering kindergarten in the U.S. are vaccinated. A school district has 180 incoming kindergarten children.

Which of the following is true concerning the shape of the sampling distribution?

• The sampling distribution is normal because n > 30

• The sampling distribution is not normal because nq is < 30

• The sampling distribution is normal because 93% of 180 is > 10

• The sampling distribution is normal because np and nq are both > 10

A realtor has been told that 43% of homeowners in a city prefer to have a finished basement. She surveys a group of 300 homeowners randomly chosen from her client list. Describe the sampling distribution model of the proportion of homeowners in this sample who prefer a finished basement.

• mean = 43%; standard deviation = 1.4%

• mean = 57%; standard deviation = 2.9%

• mean = 57%; standard deviation = 1.4%

• mean = 43%; standard deviation = 2.9%

• There is not enough information to describe the distribution.

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

Would it be unusual to get a sample proportion of .35 or higher? Explain

• Yes because only 10 of the sample proportions 0.35.

• No because 23/100 of the sample proportions were 35% or higher. 23% is not unusual

• Yes because we should get 25% every time.

Select the correct description

• Average Percent

• Population Proportion

• Sample Proportion

• Percent Slope of a Distribution

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

• 0.8354

• 0.1398

• 0

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

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

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 probability that more than 95% of the orders are delivered within three working days?

• 0.0228

• 0.4779

• 0.0478

• 0.9522