Sampling Distributions of Proportions

According to government data, 22% of American children under the age of six live in households with incomes less than the official poverty level. A study of learning in early childhood chooses an SRS of 400 children. What is the probability that at most 16% of children live in households with less than the official poverty level?

• 0.0003

• 0.0019

• 0.9968

• 0.9999

• 0

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. What is the probability that 38.56% or fewer went to church last week?

• 0.9999998

• 0.8929

• 0.1071

• 0.3541

According to government data, 22% of American children under the age of six live in households with incomes less than the official poverty level. A study of learning in early childhood chooses an SRS of 300 children.

Are the conditions/assumptions for normality met?

• Yes, all of them are met.

• No, the sample is not random

• No, we have less than 10 successes

• No, 300 is more than 10% of all children

According to government data, 22 percent of children in the United States under the age of 6 years live in households with incomes that are classified at a particular income level. A simple random sample of 300 children in the United States under the age of 6 years was selected for a study of learning in early childhood. If the government data are correct, which of the following best approximates the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level? (Note: z represents a standard normal random variable.)

• 
• 
• 
• 
• 

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.

The mean of the sampling distribution (for proportions of vaccinated children) would be _____.

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.

The standard deviation of the sampling distribution (for proportions of vaccinated children) would be _____.
(Round answers to three or four decimal places.)

According to the Center for Disease Control, 93% of children entering kindergarten in the U.S. are vaccinated. Find the z-score associated with a sample of 180 children in which 162 have been vaccinated.

• -1.34

• 1.34

• .0901

• .9099

According to the Center for Disease Control, 93% of children entering kindergarten in the U.S. are vaccinated. Find the probability that a sample of 16 children would have fewer than 14 vaccinated.

• -1.34

• 1.34

• .0901

• .9099