Sampling Distribution Counts

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

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

A state trooper randomly selects 50 cars driving on the freeway, records the state identified on the license plate, and calculates the proportion of cars with out-of-state plates. Which of the following describes the sampling distribution of the sample proportion in this context?

• The distribution of state for all cars in the troopers sample of cars on the freeway

• The distribution of state for all cars passing on this freeway

• The distribution of the proportion of cars with out-of-state plates in all possible samples of 50 cars on this freeway

• The distribution of the proportion of cars with out-of-state plates in the trooper's sample of 50 cars on this freeway

Students in a statistics class participated in a project in which they attempted to estimate the true mean height of all students in their large high school. The students were split into 4 groups. Each group had their own sampling method, and they used it to select a sample each day for 50 days. Shown above are the estimates based on their 50 samples. After the samples were collected and the means were plotted the teacher visited the school nurse who told her that the true mean height of all students in the school is 67.5 inches. Which group produced sample statistics that estimated the true value of the parameter with relatively low bias and low variability?

• Group 1

• Group 2

• Group 3

• Group 4

Given the three graphs of sampling distributions, label which graph has which sample sizes.

a

b

c

n = 30

n = 100

n = 300

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population

• The Sample

• The sampling distribution (mean)

• The sampling distribution (proportion)

The histogram represents data obtained after a census of an entire population. The sampling distribution of the sample mean based on samples of size 2 were simulated, and a histogram of the results was produced. Which of the following histograms is most likely the histogram of that sampling distribution?

• 
• 
• 
• 
• 

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population

• The sample

• The sampling distribution (mean)

• The sampling distribution (proportion)

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population

• The Sample

• The Sampling Distribution

Students in a statistics class participated in a project in which they attempted to estimate the true mean height of all students in their large high school. The students were split into 4 groups. Each group had their own sampling method, and they used it to select a sample each day for 50 days. Shown above are the estimates based on their 50 samples. After the samples were collected and the means were plotted the teacher visited the school nurse who told her that the true mean height of all students in the school is 67.5 inches. Which group produced sample statistics that estimated the true value of the parameter with relatively low bias and low variability?

• Group 1

• Group 2

• Group 3

• Group 4