Sampling Distribution Test

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

The mean and standard deviation of a population are 200 and 20, respectively. Sample size is 25. 
What is the mean of the sampling distribution?

• 200
• 16
• 25
• 4

The mean and standard deviation of a population are 200 and 20, respectively. Sample size is 25. 
What is the standard deviation of the sampling distribution?

• 200
• 16
• 25
• 4

The average cost for a gallon of gasoline is $2.51 (source AAA.org) with a standard deviation of $0.42. Find the mean and standard error of the sampling distribution if n = 49

• μ_x-bar = 2.51, σ_x-bar = 0.06
• μ_x-bar = 0.358, σ_x-bar = 0.06
• μ_x-bar = 2.51, σ_x-bar = .42

• μ_x-bar = 2.51, σ_x-bar = 0.857

Taxi fares in New York City are normally distributed with a mean fare of $22.50 and a standard deviation of $2.20. A tourism agency surveys 25 of its clients who have recently traveled to New York City to determine whether or not this information is accurate.

Recently a sample of 25 tourists reported an average taxi fare of $23.20. What is the probability that a sample of 25 would have an average taxi fare greater than $23.20 ?

• .3752

• .6248

• .0559

• .9441

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 between 15% and 25% of children live in households with less than the official poverty level?

• 0.9998

• 0.0007

• 0.9259

• 1

• 0

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

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 10% of 180 is > 10

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

For the population of farm workers in New Zealand, suppose that weekly income has a distribution with a mean of µ = $500 and a standard deviation of σ = $160. A survey of 100 farm workers is taken, including information on their weekly income.

What is the probability that a randomly selected worker has an income of at most $530?

• 0.0304

• 0.9696

• 0.4591

• 0.318

• ~0

Suppose the teenagers that attend public high schools get an average of 5.7 hours of sleep each night with a standard deviation of 1.7 hours.  What is the probability that a randomly selected group of 35 high school students get more than 6 hours of sleep each night?

• .430
• .148
• .281
• .087