AP Statistics Sampling Distributions

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

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

• The Population

• The Sample

• The Sampling Distribution

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

At a particular college, 78% of all students are receiving some kind of financial aid.The school newspaper selects a random sample of 100 students and 72% of the respondents say they are receiving some sort of financial aid. Which of the following is true?

•  78% is a population and 72% is a sample.

• 72% is a population and 78% is a sample

• 78% is a parameter and 72% is a statistic

• 72% is a parameter and 78% is a statistic

A machine fills bottles of shampoo, the amount poured has a mean of 16 oz and standard deviation 0.5 oz. A sample of 30 shampoo bottles has a mean of 15.8 oz. What is the probability of getting a mean weight of less than 15.8 oz?

• 0.99

• 0.66

• 0.34

• 0.01

A machine fills bottles of shampoo, the amount poured has a mean of 16 oz and standard deviation 0.5 oz. A sample of 30 shampoo bottles has a mean of 15.8 oz. What is the probability of getting a mean weight of less than 15.8 oz?

• 0.99

• 0.66

• 0.34

• 0.01

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

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

A ________ is a probability distribution of a statistic computed from a sample taken from a population.

• Parameter

• Central Limit Theorem

• Confidence Interval

• Sampling distribution.

Researchers are studying populations of two squirrels, the eastern gray and the western gray. For the eastern gray squirrel, about 22 percent of the population weighs over 0.5 kilogram (kg)(kg). For the western gray squirrel, about 36 percent of the population weighs over 0.5 kgkg. A random sample of 60 squirrels will be selected from the population of eastern gray squirrels, and a random sample of 120 squirrels will be selected from the population of western gray squirrels. What is the mean of the sampling distribution of the difference in sample proportions (eastern minus western) ?

Answer explanation

The mean of the sampling distribution of the difference in sample proportions for eastern minus western is equal to the difference in the population proportions, which equals 0.22−0.36