Sampling Distributions for Proportions

Suppose we have a population that is 49% male.  If we take a random sample from that population and determine the percent of our sample that is male, we refer to this proportion as...

• p

• p-hat
  

• the sample mean

• the sampling distribution

A sample is taken of 200 people. The number of people who own a dog was 80.
What is the sample proportion?

• 80

• 0.8

• 0.4

• 35%

30% of all dogs in a city are micro-chipped. In a sample of 500 dogs, what is the probability that less than 140 dogs are micro-chipped? Select the closest option.

• 0.25

• 0.21

• 0.17

• 0.13

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.)

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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

Which of the following pairs of sample size n and population proportion p would produce the greatest standard deviation for the sampling distribution of a sample proportion p?

• n = 1,000 and p close to 0

• n = 1,000 and p close to 1

• n = 1,000 and p close to 1/2

• n = 100 and p close to 0

• n = 100 and p close to 1/2

Suppose that 25 percent of women and 22 percent of men would answer yes to a particular question. In a simulation, a random sample of 100 women and a random sample of 100 men were selected, and the difference in sample proportions of those who answered yes, was calculated. The process was repeated 1,000 times. Which of the following is most likely to be a representation of the simulated sampling distribution of the difference between the two sample proportions?

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28% of all Dacula students believe Monday will be a 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

Tags

(SR.DSR.4.3